2 Step-by-Step please This is a past assignment and I will have a 2016 Assignment following soon. Need within 15 days. 1) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a freshman who lives in a dormitory? A) 0.28 B) 0.32 C) 0.52 D) 0.38 2) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a sophomore who does not live in a dormitory? A) 0.28 B) 0.1 C) 0.5 D) 0.3 3) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a junior who does not live in a dormitory? A) 0.128 B) 0.155 C) 0.112 D) 0.312 4) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a junior or senior who lives in a dormitory? A) 0.028 B) 0.096 C) 0.055 D) 0.023 5) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What percentage of the students' lives in a dormitory? A) 0.728 B) 0.628 C) 0.586 D) 0.526 6) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What percentage of the students does not live in a dormitory? A) 0.287 B) 0.147 C) 0.474 D) 0.574 7) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. If a randomly selected student lives in the dormitory, what is the probability that the student is a freshman? A) 0.284 B) 0.154 C) 0.554 D) 0.532 8) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. If a randomly selected student lives in the dormitory, what is the probability that the student is not a freshman? A) 0.468 B) 0.268 C) 0.586 D) 0.386 9) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. If a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior? A) 0.281 B) 0.641 C) 0.782 D) 0.341 10) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. Determine whether "the class status of a student" and "whether the student lives in a dormitory" are independent? A) not independent B) dependent 11) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a company is selected at random, what is the probability that the company offers stock options to their board members? A) 0.2249 B) 0.3256 C) 0.4256 D) 0.6825 12) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a company is selected at random, what is the probability that the company is small to midsized and does not offer stock options to their board members? A) 0.6532 B) 0.3713 C) 0.2382 D) 0.3562 13) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a company is selected at random, what is the probability that the company is small to midsized or offers stock options to their board members? A) 0.5632 B) 0.6539 C) 0.5962 D) 0.6879 14) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a randomly selected company is a large company, what is the probability that it offers stock options to their board members? A) 0.6542 B) 0.3466 C) 0.3645 D) 0.2116 15) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a randomly selected company offers stock options to their board members, what is the probability that it is a large company? A) 0.5618 B) 0.4819 C) 0.6268 D) 0.2368 16) Veronderstel dat in 'n ewekansige steekproef van huishoudings, daar 'n 10% kans is dat die hoof van die huishouding werkloos is. As 'n ewekansige steekproef van 5 huishoudings nou geneem word, wat is die moontlikheid dat presies een persoon werkloos is? / Suppose that in a sample of randomly selected households, there is a 10% chance that the head of the household is unemployed. If a random sample of 5 households is selected what is the probability that exactly one person is unemployed? A) 0.1000 B) 0.2 C) 0.3281 D) 0.9 E) 0.6720 17) Veronderstel dat in 'n ewekansige steekproef van huishoudings, daar 'n 10% kans is dat die hoof van die huishouding werkloos is. As 'n ewekansige steekproef van 5 huishoudings nou geneem word, wat is die moontlikheid dat al 5 van die hoof broodwinners wel werke het. / Suppose that in a sample of randomly selected households, there is a 10% chance that the head of the household is unemployed. If a random sample of 5 households is selected what is the probability that all 5 heads are employed? A) 0.1000 B) 1 C) 0.00001 D) 0.5905 E) 0.4095 18) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat 'n maksimum van 3 van die volgende 6 diefstalsake wat gerapporteer word in die stad, nie 'n gevolg is van die tekort aan geld vir alkohol nie? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that the at most 3 of the next 6 theft cases reported in this city did not result from the need for money to buy alcohol? A) 0.1536 B) 0.2765 C) 0.4557 D) 0.8208 E) 0.1792 19) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat presies 2 van die volgende 4 diefstalsake wat gerapporteer word in die stad, nie 'n gevolg is van die tekort aan geld vir alkohol nie? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that the exactly 2 of the next 4 theft cases reported in this city did not result from the need for money to buy alcohol? A) 0.5248 B) 0.1792 C) 0.4 D) 0.6544 E) 0.3456 20) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat 'n maksimum van 2 van die volgende 4 diefstalsake wat gerapporteer word in die stad, 'n gevolg is van die tekort aan geld vir alkohol? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that the at most 2 of the next 4 theft cases reported in this city resulted from the need for money to buy alcohol? A) 0.3456 B) 0.8208 C) 0.5248 D) 0.1792 E) 0.4752 21) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat minder as 3 van die volgende 4 diefstalsake wat gerapporteer word in die stad, nie 'n gevolg is van die tekort aan geld vir alkohol nie? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that less than 3 of the next 4 theft cases reported in this city did not result from the need for money to buy alcohol? A) 0.1792 B) 0.8208 C) 0.6000 D) 0.6912 E) 0.3088 22) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat ten minste 2 van die volgende 4 diefstalsake wat gerapporteer word in die stad, 'n gevolg is van die tekort aan geld vir alkohol? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that at least 2 of the next 4 theft cases reported in this city resulted from the need for money to buy alcohol? A) 0.3456 B) 0.6544 C) 0.8208 D) 0.1792 E) 0.1296 23) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat presies 3 van die volgende 4 diefstalsake wat gerapporteer word in die stad, 'n gevolg is van die tekort aan geld vir alkohol? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that exactly 3 of the next 4 theft cases reported in this city resulted from the need for money to buy alcohol? A) 0.3456 B) 0.0221 C) 0.0332 D) 0.2074 E) 0.0553 24) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die waarskynlikheid dat 'n maksimum van ses mense die toernooi bygewoon het. / A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the probability that at most six people went to the tournament. Positive response Probability 0 1 2 3 4 5 6 7 8 0.005 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 A) 0.04 B) 0.96 C) 0.54 D) 0.5 E) 0.48 25) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die waarskynlikheid dat 'n maksimum van drie mense die toernooi bygewoon het. / A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the probability that at most three people went to the tournament. Positive response Probability 0 1 2 3 4 5 6 7 8 0.005 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 A) 0.05 B) 0.14 C) 0.09 D) 0.86 E) 1 26) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die waarskynlikheid dat presies vyf mense die toernooi bygewoon het. / A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the probability that exactly five people went to the tournament. Positive response 1 2 3 4 5 6 7 8 0.005 Probability 0 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 A) 0.625 B) 0.02 C) 0.455 D) 0.05 E) 0.45 27) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die waarskynlikheid dat 'n maksimum van vyf mense die toernooi bygewoon het. / A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the probability that at most five people went to the tournament. Positive response 1 2 3 4 5 6 7 8 0.005 Probability 0 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 A) 0.02 B) 0.56 C) 0.455 D) 0.625 E) 0.46 28) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die waarskynlikheid dat ten minste vyf mense die toernooi bygewoon het. / A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the probability that at least five people went to the tournament. Positive response 0 Probability 0.005 A) 0.02 B) 0.56 C) 0.44 D) 0.625 E) 0.46 1 2 3 4 5 6 7 8 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 29) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die variansie./ A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the variance. Positive response 0 Probability 1 2 3 4 5 6 7 8 0.005 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 A) 4.8668 B) 33 C) 5.615 D) 32.5282 E) 36.395 30) 'n Navorser beplan om 'n ewekansige steekproef van 8 mense te vra of hulle die sokker toernooi bygewoon het. Die onderstaande tabel gee die waarskynlikheidsverdeling. Bereken die gemiddeld. / A researcher plans to ask 8 randomly selected people if they went to the soccer tournament. The table below shows the probability distribution. Calculate the mean. Positive response 0 1 2 3 4 5 6 7 8 Probability 0.045 0.04 A 0.3 0.02 0.04 0.2 0.3 0.005 A) 4.8668 B) 33 C) 5.615 D) 31.5282 E) 36.395 31) As z = 3 , dan is die oppervlak onder die standaardnormaalkurwe gelyk aan: / If z = 3 , the area under the standard normal curve is equal to: A) 0.6179 B) 0.9987 C) 0.7580 D) 0.9995 32) As X N ( =50 ; 2 =15 ) , dan is die modus van X gelyk aan: / If , then the mode of X is equal to: A) 50 B) 15 C) 502 D) 225 X N ( =50 ; 2 =15 ) E) 150 33) Die oppervlak onder die standaardnormaalkurwe regs van z = 1.5 is: / The area under the standard normal curve to the right of z = 1.5 is: A) 0.9332 B) 0.6915 C) 0.3085 D) 0.0668 34) Die oppervlak onder die standaardnormaalkurwe links van z = 2 is: / The area under the standard normal curve to the left of z = 2 is: A) 0.9772 B) 0.0227 C) 0.9987 D) 0.9959 35) As X N ( =50 ; =15 ) , dan is die variansie van X gelyk aan: / If X N ( =50 ; =15 ) , then the variance of X is equal to: A) 50 B) 15 C) 502 D) 225 E) 150 36) As X N ( =50 ; =15 ) , dan is die gemiddelde van X gelyk aan: / If X N ( =50 ; =15 ) , then the mean of X is equal to: A) 15 B) 152 C) 502 D) 50 E) 150 37) As X N ( =50 ; 2 =15 ) , dan is die mediaan van X gelyk aan: / If X N ( =50 ; 2 =15 ) , then the median of X is equal to: A) 50 B) 15 C) 502 D) 225 E) 150 38) As X N ( =50 ; 2 =15 ) , dan is die standaardafwyking van X gelyk aan: / If X N ( =50 ; 2 =15 ) , then the standard deviation of X is equal to: A) 50 B) 3.87 C) 502 D) 225 E) 150 X N ( =80 ; 2=36 ) , / 39) Die diastoliese bloeddruk van 100 volwasse mans is verdeel as Diastolic blood pressure measurements of 100 adult males is distributed as X N ( =80 ; 2=36 ) , Hoeveel mans het 'n bloeddruk van tussen 75 en 85? / How many males have a blood pressure of between 75 and 85? A) 50 B) 60 C) 70 D) 84 40) P( Z>3.18) A) 0.8974 B) 0.9993 C) 0.7455 D) 0.9254 E) 0.0237 41) By using the data in the table below, calculate for 2006 with 2004 as base year: / Deur gebruik te maak van die data in die onderstaande tabel bereken vir 2006 met 2004 as basis jaar: Product I 2004 P0 q0 R 5 80 2006 p1 q1 R6 60 II R8 90 R9 100 III Total R6 A 70 R5 B 80 p1q0 p0q0 p1q1 p0q1 C D E F The price index for product II. / Die prys indeks vir produk II A) 100 B) 124.87 C) 104.29 D) 128.80 E) 112.5 42) The price index of product II from 2004 to 2006 : / Die prys indeks van produk II vanaf 2004 tot 2006: A) increase B) decrease C) not a or b 43) The value of A. / Die waarde van A. A) 12 B) 28 C) 19 D) 30 E) 15 44) The value of C. / Die waarde van C. A) 1770 B) 1640 C) 1560 D) 1240 E) 1530 45) The value of D. / Die waarde van D. A) 1810 B) 1260 C) 1480 D) 1540 E) 1920 46) The value of E. / Die waarde van E. A) 1660 B) 1218 C) 1414 D) 1140 E) 1124 47) Laspeyres price index with 2004 as base. / Laspeyres prysindeks met 2004 as basis. A) 97.14 B) 120.5 C) 94.85 D) 122.20 E) 106.49 48) Paasche price index with 2004 as base. / Paasche prysindeks met 2004 as basis. A) 105.06 B) 114.91 C) 110.75 D) 99.13 E) 119.50 49) Unweighted price index with 2004 as base. / Ongeweegde prysindeks met 2004 as basis. A) 92.15 B) 128.59 C) 120.84 D) 105.26 E) 109.39 After some consideration it has been decided to change the base year for the fuel index from 2001 to 2005. / Na sekere oorwegings is daar besluit om die basis jaar van die brandstof indeks te verander van 2001 na 2005. The old index numbers were: / Die ou indeks getalle was: (2001=100) 1998 1999 2000 2001 2002 2003 2004 2005 2006 (2005=100) 70 78 90 100 110 115 124 130 134 A B C D E F G H I 50) The value of A. / Die waarde van A. A) 72.25 B) 53.85 C) 82.23 D) 66.67 E) 42.35 51) The value of C. / Die waarde van C. A) 82.33 B) 70.23 C) 50.33 D) 42.33 E) 69.23 52) The value of E. / Die waarde van E. A) 110.67 B) 120.67 C) 75.44 D) 84.62 E) 70.67 53) The value of H. / Die waarde van H. A) 134.69 B) 103.37 C) 145.63 D) 116.67 E) 100 54) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is ________ minutes. A) 80 B) 64 C) 1600 D) 40 55) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling distribution of the sample mean is ________ minutes. A) 40 B) 5 C) 1600 D) 0.625 56) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is ________. A) 0.2444 B) 0.7566 C) 0.3446 D) 0.6554 57) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be between 77 and 89 minutes is ________. A) 0.8554 B) 0.1446 C) 0.6898 D) 0.2462 58) A study at a college on the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is ________ that between 30% and 50% of the students in the sample will be minority students. A) 0.9548 B) 0.8034 C) 0.1254 D) 0.2268 59) A study at a college on the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is ________ that more than half of the students in the sample will be minority students. A) 0.8188 B) 0.9451 C) 0.1922 D) 0.2954 60) A study at a college on the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ________% of minority students. A) 55.24 B) 45.65 C) 40.26 D) 49.83 61) A study at a college on the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, 95% of the samples will have more than ________% of minority students. A) 30.25 B) 35.55 C) 40.55 D) 45.66 PAST TEST 1 - need within 10 - 15 days please YOU WILL SEE THAT THE CORRECT ANSWERS IS MARKED * I need the step-by-step explanation please as this is the MEMO. Your statistics lecturer decides to select a random sample of 129 EBBCS students to complete a questionnaire. The number of students in each of the 5 lecturers' classes is given in the table below. LECTURER / NUMBER OF STUDENTS / 1 2 3 4 5 1. If a stratified random sample is drawn from each class, what is the sample size of Lecturer 1? (a) 25 2. (b) 11 (c) 33 * (d) 129 If a stratified random sample is drawn from each class, what is the sample size of Lecturer 3? (a) 25 3. 325 289 105 239 301 (b) 11 * (c) 33 (d) 129 If a stratified random sample is drawn from each class, what is the sample size of Lecturer 4? (a) 11 (b) 25 * (c) 33 (d) 129 4. Given a population of 1500, select a systematic sample of 10 with starting point 35. What is the value of the first sample observation? (a) 35* (b) 635 (c) 150 (d) 185 5. Given a population of 1500, select a systematic sample of 10 with starting point 35. What is the value of the fifth sample observation? (a) 35 (b) 635 * (c) 150 (d) 185 Consider the following data: 21 21 11 33 29 18 19 27 15 13 25 15 15 19 20 20 18 21 32 26 25 26 20 30 22. If we use Sturge's formula, how many class intervals would there be? (a) 10 (b) 6 * (c) 5.5 (d) 20 (c) 5.5 (d) 10 23. Determine the width of the classes. (a) 4 * (b) 5 24. What percentage of the data is greater than 20? (a) 50% * (b) 63% (c) 100% (d) 55% Now construct now a frequency distribution by using a class width of 5 and by taking the lower limit of the first interval as 10. Intervals / [ [ [ [ [ B ) - A) ) ) ) Frequency / C D 25. What is the value of A in above table? (a) 10 (b) 15 (c) 20 * (d) 25 (c) 20 (d) 30 * (c) 6 (d) 3 (c) 6 * (d) 3 26. What is the value of B in above table? (a) 15 (b) 20 27. What is the value of C in above table? (a) 2 * (b) 7 28. What is the value of D in above table? (a) 2 (b) 7 29. What is the sample size, n, in above table? (a) 20 (b) 24 * (c) 30 (d) 25 The following frequency distribution was constructed. Now answer the following questions: Intervals / Class Midpoints / Frequencies / Cumulative frequency / [ 3 - 9) [ 9 - 15 ) [ 15 - A ) [ A - 27 ) [ 27 - 33 ) 6 B 18 24 C D 2 7 17 22 25 E F G 30. What is the sample size? (a) 10 (b) 17 (c) 25 * (d) 5 (c) 12 (d) 2 (c) 12 * (d) 30 (c) 12 (d) 30 * (c) 6 (d) 2 * (c) 5 * (d) 3 (c) 0.2 * (d) 0.4 31. What is the value of A? (a) 21 * (b) 17 32. What is the value of B? (a) 21 (b) 17 33. What is the value of C? (a) 21 (b) 17 34. What is the value of D? (a) 3 (b) 9 35. What is the value of E? (a) 2 (b) 10 36. What is the value of F? (a) 0.5 (b) 1 37. What is the value of G? Relative frequency / (a) 0.12 * (b) 0.2 (c) 0.3 (d) 1 38. The sum of all the relative frequencies is always __________ . (a) 1 * (b) 90% Consider the following data: 6 10 4 (c) 25 3 7 9 (d) 0% 21 14 Now answer now the following questions: 39. The range of the above is:: (a) 18 * (b) 21 (c) 6 (d) 14 (c) 9.25* (d) 18 (c) 9.25 (d) 18 (b) 5 (c) 8 * (d) 34.81 (b) 34.79 * (c) 9.25 (d) 18 (c) 14 (d) 4 (c) 14 (d) 4.5 * (c) 14 (d) 4 40. The mean of the data is: (a) 5.90 (b) 8 41. The standard deviation: (a) 5.90 * (b) 34.81 42. The median: (a) 9.25 43. The variance is : (a) 5.90 44. The position of the third quartile: (a) 6.75 * (b) 2 45. The value of the first quartile: (a) 6 (b) 2 46. The interquartile range (a) 8.5 * (b) 2 47. The coefficient of variation (%) (a) 34.81 (b) 5.90 (c) 8 (d) 63.78 * Telephone calls arriving at a switchboard are answered by the telephonist. The following table gives the frequency distribution of the time, to the nearest second, taken by the telephonist to answer the calls received during one day: Time to answer (to nearest second) / Number of calls / [ 10 - 20 ) [ 20 - 30 ) [ 30 - 40 ) [ 40 - 50 ) [ 50 - 60 ) 20 35 30 10 5 48. The average amount of time (in seconds) taken by the telephonist to answer a call is: (a) 29.5 * (b) 30 (c) 50 (d) 175 49. The median of the amount of time (in seconds) taken by the telephonist to answer a call is: (a) 29.5 (b) 28.5714 * (c) 30 (d) 35 50. The standard deviation of the amount of time (in seconds) taken by the telephonist to answer a call is: (a) 50 (b) 10.7661 * (c) 23.64 (d) 115.9091 51. The variance of the amount of time (in seconds) taken by the telephonist to answer a call is: (a) 50 (b) 10.7661 (c) 23.64 (d) 115.9091 * (b) 28.5714 (c) 21.4286 (d) 15.2381 (b) 28.5714 (c) 21.4286 * (d) 15.2381 (c) 21.4286 (d) 15.2381 * 52. The third quartile. (a) 36.6667 * 53. The first quartile. (a) 36.6667 54. The interquartile range. (a) 36.6667 (b) 28.5714 55. The eighty seventh percentile. (a) 36.6667 (b) 28.5714 (c) 42 * (d) 29.5 (b) 50 * (c) 42 (d) 29.5 56. The range. (a) 36.6366 57. What is the shape of the distribution? (a) Positive skew * (b) Symmetrical (c) Negative skew 58. The marks of a Grade 8 mathematics class is normally distributed with a mean of 48 and a standard deviation of 8. By using the empirical rule, what is the estimated percentage of learners that will score between 40 and 64 in a test? (a) 34% (b) 47.5% (c) 69.8% (d) 81.5% * 59. The marks of a Grade 8 mathematics class is normally distributed with a mean of 48 and a standard deviation of 8. By using the empirical rule, what is estimated percentage of learners that will score between 64 and 72 in a test? (a) 2.35% * (b) 47.5% (c) 0.15% (d) 95% 60. The marks of a Grade 8 mathematics class is normally distributed with a mean of 48 and a standard deviation of 8. By using the empirical rule, what is estimated percentage of learners that will score less than 24 in a test? (a) 2.85% (b) 34% (c) 0.15% * NEXT PAGE PLEASE (d) 80% EXAM 1 PAST EXAM PAPER MEMO WITH ANSWERS I NEED STEP-BY STEP WITHIN 10 - 15 DAYS The marks that a class get for a test out of 40 are as follows: 24 19 21 27 20 17 17 32 22 26 18 13 23 30 10 13 18 22 34 16 18 23 15 19 28 25 25 20 17 15 {Choose the first class interval lower limit to be 10 and the class width to be 5. 6. Define the random variable. (a) Marks obtain. (b) Class average. (c) Out of 40 marks. (d) Test. From the data set above, find, in the table below, the absolute frequency distribution, the relative frequency distribution and the cumulative frequency distribution. Answer questions 7 to 10 from the table. Intervals / Absolute frequency / [ - ) [ - ) [ - ) [ - Cumulative frequency / ) [ Relative frequency / Total A D C B 7. What is the value of A in the table? (a) 5 8. (b) 9 (b) 40 (e) 10 (d) 32 (e) 25 (d) 0.2 (e) 1 (d) 27 (c) 30 (e) 30 What is the value of C in the table? (a) 0.37 10. (d) 11 What is the value of B in the table? (a) 18 9. (c) 8 (b) 0.27 (c) 0.17 What is the value of D in the table? (a) 8 (b) 22 (c) 11 A restaurant owner randomly selected and recorded the value of meals enjoyed by 15 diners on a given day. Answer questions 11 - 24 . The values of meals were (rounded to the nearest rand): / 25 25 11. 80 28 34 40 26 21 65 28 25 39 Define the random variable. (a) Owner observation. (b) Average.. (c) Value of meals.. (d) Number of diners.. 12. Define the data type. {Nominal, Ordinal, Discrete, Continuous} (a) Nominal (b) Ordinal (c) Discrete / (d) Continuous / Kontinue 13. Find the arithmetic mean. /. (a) 35 14. (e) 25 (b) 8 (c) 28 (d) 39 (e) 59 (b) 30 (c) 35 (d) 12 (e) 25 (c) 39 (d) 25 (e) 35 Find the lower quartile.. (a) 4 17. (d) 28 Find the mode.. (a) 28 16. (c) 15 Find the median.. (a) 25 15. (b) 30 (b) 12 Find the third quartile. 25 30 34 (a) 39 18. (b) 20.98 (c) 15.70 (d) 16.41 (e) 18.04 (b) 325.62 (c) 288.42 (d) 216.89 (e) 246.58 (b) 59 (c) 39 (d) 25 (e) 45 (d) 52.57% (e) 44.86% Find the coefficient of variation. (a) 42.08 22. (e) 30 Find the range. (a) 35 21. (d) 15 Find the variance. (a) 269.14 20. (c) 36 Find the sample standard deviation.. (a) 14.73 19. (b) 12 (b) 48.51% (c) 46.87% Are the data positive skewed or negative skewed or symmetrical? / (a) positive skewed / (b) negative skewed / (c) symmetrical / 23. Find the interquartile range.. (a) 24 24. (c) 30 (d) 39 (e) 14 Write down the five-number summary. Which one is incorrect?. (a) 21 25. (b) 34 (b) 25 (c) 28 (d) 39 (e) 30 Which one of the following values cannot be a probability of an event? (a) 0.999 (b) 8 6 (c) 0.46 (d) 1 5 (e) 0.8 A container is filled with 5 bottles of white wine, 3 bottles of red wine and 1 bottle of grape juice. The bottles are identical, except for the contents of the bottles. Answer questions 26 and 27. / 26. If two bottles are drawn without replacement from the container, the probability that both of the bottles contain white wine is.. (a) 6 72 (e) 27. 60 72 (b) 02361 (d) 3 72 20 72 (c) 0.2222 (d) 0.1975 (e) 0.1111 (f) 0.0988 (b) Veranderlike / Variable (c) Waarneming / Observation (e) Nominaal / Nominal (f) Diskreet / Discrete A ..................... is the collection of all the observations of a random variable under study on which one is trying to draw conclusions in practice.. (a) Steekproefeenheid / Sampling unit (c) Steekproef / Sample (e) Waarneming / Observation 30. 9 72 Any characteristic being measured or observed is called a ...................... / (a) Data / Data (d) Waarde / Value 29. (f) (c) If two bottles are drawn with replacement from the container, the probability that one of the bottles contain grape juice is. (a) 0.2099 28. 12 72 (b) (b) Populasie / Population (d) Eksperimentering / Experimentation (f) Waarde / Value A dice is rolled once; determine the probability of event A: observe a number less than 4 (a) 25 (b) 1/6 (c) 4/6 (d) 3/6 (e) 0.6 The following table shows the 300 employees of a small manufacturing company cross-classified on the basis of age and work category. Age / Ouderdom Work category / Werk-kategorie Total / Totaal Production Sales Office Produksie Verkope Kantoor < 25 50 2 50 C 25 - 40 A 24 50 144 > 40 40 4 10 54 Total / Totaal 160 B 110 300 31. What is the value of A in the table? / Wat is die waarde van A in die tabel? (a) 60 32. 0.01 3 (c) 60 (d) 70 (e) 54 (b) 0.18 (c) 0.24 (d) 0.48 (e) 0.82 (d) 0.133 (e) 0.275 (b) 0.423 (c) 0.543 (b) 0.16 (c) 0.3 6 0.4 6 (d) (e) 0.96 P( > 40 given Office) / P( > 40 gegee kantoor) (a) 0.09 37. (b) 40 P( Sales or Office) / P( Verkope of kantoor) (a) 140 36. (e) 144 P( Sales and > 40) / P( Verkope en > 40) (a) 35. (d) 80 P( 25 - 40) (a) 0.08 34. (c) 50 What is the value of B in the table? / Wat is die waarde van B in die tabel? (a) 30 33. (b) 70 (b) 0.47 (c) 0.37 (d) 0.51 (e) 0.53 P( Production or 25 - 40) / P( Produksie of 25 - 40) (a) 0.78 (b) 0.84 (c) 0.67 (d) 0.59 (e) 0.41 The following table contains the probability distribution for the number of traffic accidents daily in a small city:. Number of accidents daily (X) 0 1 2 3 4 5 38. P(X) 0.1 0.2 0.45 0.15 0.05 0.05 Find E(X) / Bepaal E(X) (a) 1 (b) 4 (c) 6 (d) 5 (e) 2 Suppose that X has a discrete binomial distribution with parameters n = 5 and p = 0.3. Answer questions 39 to 42.. 39. Determine / Bereken P( X = 5) (a) 0.04483 40. (d) 0.1681 (e) 0.4165 (c) 0.7667 (d) 0.9976 (e) 0.4551 (c) 5 (d) 2.8 (e) 3.2 (c) 1.67 (b) 0.8564 (d) 2.59 (e) 1.05 E(X) Find / Bepaal (a) 1.5 42. (c) 0.0258 Determine / Bereken P( X < 5) (a) 0.7988 41. (b) 0.00243 (b) 2 Find / Bepaal Var ( X ) (a) 3.78 (b) 2.85 Given that Z has a standard normal distribution, determine: / Gegee dat Z 'n standaard normaalverdeling het, bepaal. Z ~ N ( 0, 1) 43. P( - 1. 25 < Z < 1.54) (a) 0.8326 44. (d) 0.9982 (e) 0.7412 (b) 0.4986 (c) 0.3997 (d) 0.8983 (e) 0.8243 (c) 0.7993 (d) 0.4993 (e) 0.6824 (c) 0.0010 (d) 0.0049 (e) 0.0456 P( Z > -2.12) : (a) 0.9830 46. (c) 0.9382 P( -2.84 < Z < - 1.28) : (a) 0.0980 45. (b) 0.1056 (b) 0.4994 P(2.52 < Z < 2.58): (a) 0.9951 (b) 0.9892 A luxury passenger train has 500 passengers on board whose ages are normally distributed around a mean of 60 years with a standard deviation of 12 years. / 47. The probability that the age of a passenger is less than 72 years . / Die waarskynlikheid dat die ouderdom van 'n passasier minder as 72 jaar is: (a) 0.0398 48. (b) 0.3413 (c) 0.8413 (d) 0.4800 (e) 0.3860 What percent of passengers are between 48 and 75 years old. / Watter persentasie van die passasiers is tussen 48 en 75 jaar oud: (a) 66.93% 49. (e) 82.64% (b) 80 (c) 65 (d) 53 (e) 72 (b) 34 (c) 86 (d) 25 (e) 72 What is the slope of the line through the points (6 ; 8) and (3 ; 1)?/ Wat is die helling van die lyn deur die punte (6 ; 8) en (3 ; 1)? (a) 3 52. (d) 73.57% How many of the passengers are older than 78 years. / Hoeveel van die passasiers is ouer as 78 jaar. (a) 64 51. (c) 46.96% How many of the passengers are between 42 and 51 years old. / Hoeveel van die passasiers is tussen 42 en 51 jaar oud. (a) 39 50. (b) 87.25% (b) 9 (c) 3 (d) - 9 (e) 7 Give the standard straight line equation of 8 x+ 2 y =142 x +3 y / Gee die standaard reguitlyn vergelyking van 8 x+ 2 y =142 x +3 y a) y=3 x+ 7 b) y=3 x7 c) y=10 x14 d) y=10 x+14 53. Gestel 'n lyn met helling 7. Wat is die helling van 'n loodlyn? / Suppose a line has slope 7 . What is the slope of any perpendicular line?/ a) 7 b) 7 c) 3.5 d) 1 7 e) 1 7 54. Mr. Corneq would like to give his daughter a cash gift of R20 000 on her 21 st birthday in exactly four years' time. How much must he deposit today in a fixed deposit account which pays 9% p.a. compounded monthly to reach his target? / a) R19 411.08 b) R14 168.50 c) R13 972.28 d) R347.70 e) R5 000 Consider the information in the following table before answering questions 55 and 56./ Beskou die inligting in die volgende tabel voordat vrae 55 en 56 beantwoord word. Mrs. Glimely took a loan of R75 000 from ABC bank for a period of 5 years. She pays a fixed amount of R4 868.02 every quarter, and 10.5% interest p.a. compounded quarterly on the principal amount. Perform an armortisation schedule for Mrs. Glimely's payments./ 55. Give the interest that Mrs. Glimely paid the second quarter./ Gee die rente wat Me. Glimely betaal het met die tweede kwartaal. a) R1 840.92 56. b) R1 968.75 c) R2 899.27 d) R2 975.38 e) R69 125.35 Find the closing balance at the end of the third quarter./ Bepaal die eindbalans aan die einde van die derde kwartaal. a) R4 868.02 57. b) R66 071.87 c) R3 053.48 d) R1 814.52 e) R60 395.94 If you buy a motorbike second hand for R11 500, and it depreciates annually by 15.5% using the balance reducing method, calculate how much you can sell it for at the end of the 3rd year (calculate the book value at the end of the 3rd year)./ a) R1 782.50 b) R6 152.50 c) R5 347.50 d) R7 935.00 e) R6 938.54 The supply and demand for beer in South Africa is given as follows: D Q =6 p +250 S Q =9 p200 Africa is hosting the FIFA World Cup, this is expected to result in a change of 5 p+1250 . After the World Cup some of the foreigners realized we do not have the best beer in South Africa and decided to introduce a new beer in Africa, this will result in a change of 150 . Now to stop the people from drinking further the government increases sin tax and these results in a fixed amount of R6 per unit sold./ D Q =6 p +250 QS =9 p200 58. The equilibrium price before the World cup is........../ Die ewewigsprys voor die Wreldbeker-sokkertoernooi, is.......... (a) 30 59. (c) 70 (d) 80 (e) 90 The quantity before the World cup is......../ Die hoeveelheid voor die Wreldbekersokkertoernooi is.......... (a) 30 60. (b) 35 (b) 35 (c) 70 (d) 80 (e) 90 A company that makes sunglasses has fixed costs of R2 100 and variable costs of R15,20 for each sunglass. What are the total and the variable costs when the company completes an order of 850 sunglasses?/ (a) TC/TK = 12 920 ; VC/VK = 15 020 (b) TC/ TK = 1 797 920 ; VC/VK = 12 920 (c) TC/TK = 2 100 ; VC/VK = 15.2 (d) TC/TK = 2115.2 ; VC/VK = 15 .2 (e) TC/TK = 15 020 ; VC/VK = 12 920 61. A firm produces goods which they can sell for an amount of R12,00 per unit. Its costs are a fixed outlay of R6 000,00 plus R9,00 in variable costs for each unit produced. Write an expression for the firm's profit in terms of the number of units produced./ (a) 12Q6 000 (d) 3 Q6 000 62. (b) 9 Q6 000 (e) 18 Q6 000 Find the simple interest rate required for an investment of R5 000 to grow to R8 000 in 4 years./ Bepaal die enkelvoudige rentekoers benodig vir 'n belegging van R5 000 om te groei tot R8 000 in 4 jaar. (a) 0.15% 63. (c) 3 Q6 000 (b) 0.6% (c) 15% (d) 1.6% (e) 5.33% Calculate the effective rate p.a. equivalent to the nominal rate of 6.75% p.a. compounded weekly./ Bereken die effektiewe rentkoers p.j. ekwiwalent tot die nominale rentekoers van 6.75% p.j weekliks saamgestel. (a) 6.98% (b) 0.069% (c) 6.75% (d) 0.1298% (e) 6.96% 64. On reaching the age of 60, an employee of company ABC has the option of receiving a pension of R8 750 per month for 5 years, payable at the end of each month or taking an equivalent lump sum gratuity on retirement. Calculate the equivalent lump sum. Assume interest is compounded monthly at 10% p.a (a) R43 750.00 (b) R525 000.00 (c) R33 169.38 (d) R42 677.47 (e) R411 821.98 Suppose you take a loan of R7 500 for 2 years, and the agreement of the loan is that you pay an interest of 9.5% p.a. compounded quarterly on the principal amount and a fixed amount of R1 040.44 at the end of at the end of every quarter./ 65. Construct an amortisation schedule for 2 years and give the principal payment of the 3rd quarter./ Konstrueer 'n aflossingskedule vir 2 jaar en gee die kapitaal betaling van die 3de kwartaal. (a) R1 040.44 (b) R393.21 66. (c) R136.68 (d) R911.74 (e) R4 851.14 Construct an amortisation schedule of five years and give the interest paid in the 4 th quarter./ Konstrueer 'n aflossingskedule vir 5 jaar en gee die rente betaal in die 4de kwartaal. (a) R609.88 (b) R115.21 (c) R1 040.44 (d) R415.97 (e) R103.99 Ian bought a P.C. for R8 500 and it was depreciated annually by 11.25% using the balance reducing method./ Ian koop 'n P.C. vir R8 500 en dit het jaarliks waarde verminder met 11.25% deur gebruik te maak van die balansvermindering metode. 67. Calculate the book value of Ian's P.C. at the end of the 2 nd year./ Bereken die boekwaarde van Ian se P.C. aan die einde van die 2de jaar. (a) R6 695.08 (b) R7 543.75 (c) R848.67 (d) R6 587.50 (e) R1 914.50 The following table gives the number of hours that 45 hospital patients slept following the administration of a certain anesthetic. / Number of hours / Aantal ure Number of Patients / Aantal pasinte F [1 - 4) [4 - 7) [7 - A) [A - 13) [13 - 16) [16 - 19) 68. (b) 8.5 (c) 7.5 (d) 8 (e) 3.3333 Calculate the median number of hours that patients slept following the administration of an anesthetic. / Bereken die mediaan aantal ure wat pasinte geslaap het n die toediening van narkose. (a) 34 70. 11 21 C D 43 E Calculate the mean number of hours that patients slept following the administration of an anesthetic. / Bereken die gemiddelde aantal ure wat pasinte geslaap het n die toediening van narkose. (a) 13 69. 11 10 B 7 2 2 (b) 4.5769 (c) 22.5 (d) 8.5 (e) 7.3462 Calculate the variance of the hours that patients slept following the administration of the anesthetic. / Bereken die variansie van die aantal ure geslaap van pasinte na die toediening van die narkose. (a) 16.7727 (b) 4.0954 (c) 55.8773 (d) 31.5 (e) 5.6125 Assignment 2 Step-by-Step please This is a past assignment and I will have a 2016 Assignment following soon. Need within 15 days. 1) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a freshman who lives in a dormitory? A) 0.28 B) 0.32 C) 0.52 D) 0.38 (35%) (80%) = (0.35) (0.80) = 0.28 2) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a sophomore who does not live in a dormitory? A) 0.28 B) 0.1 C) 0.5 D) 0.3 (25%) (1 - 60%) = (0.25) (0.40) = 0.10 3) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a junior who does not live in a dormitory? A) 0.128 B) 0.155 C) 0.112 D) 0.312 (16%) (1 - 30%) = (0.16) (0.70) = 0.112 4) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected student is a junior or senior who lives in a dormitory? A) 0.028 B) 0.096 C) 0.055 D) 0.023 (16%) (30%) + (24%) (20%) = (0.16) (0.30) + (0.24) (0.20) = 0.096 5) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What percentage of the students' lives in a dormitory? A) 0.728 B) 0.628 C) 0.586 D) 0.526 (35%) (80%) + (25%) (60%) + (16%) (30%) + (24%) (20%) = 0.526 6) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What percentage of the students does not live in a dormitory? A) 0.287 B) 0.147 C) 0.474 D) 0.574 1 - 0.526 = 0.474 7) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. If a randomly selected student lives in the dormitory, what is the probability that the student is a freshman? A) 0.284 B) 0.154 C) 0.554 D) 0.532 (35%) (80%)/0.526 = 0.28/0.526 = 0.532 8) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. If a randomly selected student lives in the dormitory, what is the probability that the student is not a freshman? A) 0.468 B) 0.268 C) 0.586 D) 0.386 1 - 0.532 = 0.468 9) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. If a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior? A) 0.281 B) 0.641 C) 0.782 D) 0.341 [(16%) (1 - 30%) + (24%) (1 -20%)] / 0.474 = 0.641 10) According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. Determine whether "the class status of a student" and "whether the student lives in a dormitory" are independent? A) not independent B) dependent The probability that a randomly selected student is a freshman who lives in a dormitory is 0.28 and it is not same as the probability that a randomly selected student is a freshman, i.e. 0.35. Therefore the two events "the class status of a student" and "whether the student lives in a dormitory" are not independent. 11) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a company is selected at random, what is the probability that the company offers stock options to their board members? A) 0.2249 B) 0.3256 C) 0.4256 D) 0.6825 83/369 = 0.2249 12) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a company is selected at random, what is the probability that the company is small to midsized and does not offer stock options to their board members? A) 0.6532 B) 0.3713 C) 0.2382 D) 0.3562 137/369 = 0.3713 13) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a company is selected at random, what is the probability that the company is small to midsized or offers stock options to their board members? A) 0.5632 B) 0.6539 C) 0.5962 D) 0.6879 180/369 + 83/369 - 43/369 = 220/369 = 0.5962 14) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a randomly selected company is a large company, what is the probability that it offers stock options to their board members? A) 0.6542 B) 0.3466 C) 0.3645 D) 0.2116 40/189 = 0.2116 15) A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their noncash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. The contingency table is as follows: If a randomly selected company offers stock options to their board members, what is the probability that it is a large company? A) 0.5618 B) 0.4819 C) 0.6268 D) 0.2368 40/83 = 0.4819 16) Veronderstel dat in 'n ewekansige steekproef van huishoudings, daar 'n 10% kans is dat die hoof van die huishouding werkloos is. As 'n ewekansige steekproef van 5 huishoudings nou geneem word, wat is die moontlikheid dat presies een persoon werkloos is? / Suppose that in a sample of randomly selected households, there is a 10% chance that the head of the household is unemployed. If a random sample of 5 households is selected what is the probability that exactly one person is unemployed? A) 0.1000 B) 0.2 C) 0.3281 D) 0.9 E) 0.6720 1 51 1 4 P ( X=1 )= 5 ( 0.10 ) ( 10.10 ) =( 5 ) ( 0.10 ) ( 0.90 ) =0.3281 1 () 17) Veronderstel dat in 'n ewekansige steekproef van huishoudings, daar 'n 10% kans is dat die hoof van die huishouding werkloos is. As 'n ewekansige steekproef van 5 huishoudings nou geneem word, wat is die moontlikheid dat al 5 van die hoof broodwinners wel werke het. / Suppose that in a sample of randomly selected households, there is a 10% chance that the head of the household is unemployed. If a random sample of 5 households is selected what is the probability that all 5 heads are employed? A) 0.1000 B) 1 C) 0.00001 D) 0.5905 E) 0.4095 5 55 5 P ( X=5 ) = 5 ( 0.90 ) (10.90 ) =( 0.90 ) =0.5905 5 () 18) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat 'n maksimum van 3 van die volgende 6 diefstalsake wat gerapporteer word in die stad, nie 'n gevolg is van die tekort aan geld vir alkohol nie? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that the at most 3 of the next 6 theft cases reported in this city did not result from the need for money to buy alcohol? A) 0.1536 B) 0.2765 C) 0.4557 D) 0.8208 E) 0.1792 3 x 4x P ( X 3 )= 6 ( 0.60 ) ( 10.60 ) =0. 4557 x x=0 () 19) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat presies 2 van die volgende 4 diefstalsake wat gerapporteer word in die stad, nie 'n gevolg is van die tekort aan geld vir alkohol nie? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that the exactly 2 of the next 4 theft cases reported in this city did not result from the need for money to buy alcohol? A) 0.5248 B) 0.1792 C) 0.4 D) 0.6544 E) 0.3456 2 42 2 2 P ( X=2 )= 4 ( 0. 6 0 ) ( 10. 6 0 ) =6 ( 0. 6 0 ) ( 0. 4 0 ) =0.34 5 6 2 () 20) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat 'n maksimum van 2 van die volgende 4 diefstalsake wat gerapporteer word in die stad, 'n gevolg is van die tekort aan geld vir alkohol? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that the at most 2 of the next 4 theft cases reported in this city resulted from the need for money to buy alcohol? A) 0.3456 B) 0.8208 C) 0.5248 D) 0.1792 E) 0.4752 2 x 4x P ( X 2 )= 4 ( 0.60 ) ( 10.60 ) =0.5248 x=0 x () 21) In 'n sekere stad is die tekort aan geld om alkohol te koop die rede vir 60% van alle diefstal. Wat is die moontlikheid dat minder as 3 van die volgende 4 diefstalsake wat gerapporteer word in die stad, nie 'n gevolg is van die tekort aan geld vir alkohol nie? / In a certain city the need for money to buy alcohol is given as the reason for 60% of all thefts. What is the probability that less than 3 of the next 4 theft cases reported in this city did not result from the need for money to buy alcohol? A) 0.1792 B) 0.8208 C) 0.6000 D) 0.6912 E) 0.3088 2 y 4 y P (Y <3 ) ( y 2 4 0. 0 10. 8 () 22) in 'n sekere stad is die tekort aan geld om alkohol te koop rede vir 60% van alle diefstal. wat moontlikheid dat ten minste volgende diefstalsake gerapporteer word stad, gevolg alkohol?>3.18) A) 0.8974 B) 0.9993 C) 0.7455 D) 0.9254 E) 0.0237 P (Z > -3.18) = P (Z 3.18) = (3.18) = 0.9993 41) By using the data in the table below, calculate for 2006 with 2004 as base year: / Deur gebruik te maak van die data in die onderstaande tabel bereken vir 2006 met 2004 as basis jaar: Product I 2004 P0 q0 R5 80 2006 p1 q1 R6 60 p1q0 480 p0q0 400 p1q1 360 p0q1 300 II R8 90 R9 100 810 720 900 800 III Total R6 A=1 9 70 240 R5 B=2 0 80 240 350 C= 1640 420 D= 1540 400 E= 1660 480 F= 158 0 The price index for product II. / Die prys indeks vir produk II A) 100 B) 124.87 C) 104.29 D) 128.80 E) 112.5 p1 9 100= 100=112. 5 p0 8 42) The price index of product II from 2004 to 2006 : / Die prys indeks van produk II vanaf 2004 tot 2006: A) increase B) decrease C) not a or b Since 112.5 is more than 100. 43) The value of A. / Die waarde van A. A) 12 B) 28 C) 19 D) 30 E) 15 44) The value of C. / Die waarde van C. A) 1770 B) 1640 C) 1560 D) 1240 E) 1530 45) The value of D. / Die waarde van D. A) 1810 B) 1260 C) 1480 D) 1540 E) 1920 46) The value of E. / Die waarde van E. A) 1660 B) 1218 C) 1414 D) 1140 E) 1124 47) Laspeyres price index with 2004 as base. / Laspeyres prysindeks met 2004 as basis. A) 97.14 B) 120.5 C) 94.85 D) 122.20 E) 106.49 p 1 q 0 100= 1,640 100=106.49 1,540 p0 q0 48) Paasche price index with 2004 as base. / Paasche prysindeks met 2004 as basis. A) 105.06 B) 114.91 C) 110.75 D) 99.13 E) 119.50 p 1 q 1 100= 1,660 100=1 05.06 1,580 p0q1 49) Unweighted price index with 2004 as base. / Ongeweegde prysindeks met 2004 as basis. A) 92.15 B) 128.59 C) 120.84 D) 105.26 E) 109.39 p 1 100= 20 100=1 0 5 .26 19 p0 After some consideration it has been decided to change the base year for the fuel index from 2001 to 2005. / Na sekere oorwegings is daar besluit om die basis jaar van die brandstof indeks te verander van 2001 na 2005. The old index numbers were: / Die ou indeks getalle was: (2001=100) 1998 1999 2000 (2005=100) 70 78 90 A B C 2001 2002 2003 2004 2005 2006 100 110 115 124 130 134 50) The value of A. / Die waarde van A. A) 72.25 B) 53.85 C) 82.23 D) 66.67 E) 42.35 70 100=53.85 1 30 51) The value of C. / Die waarde van C. A) 82.33 B) 70.23 C) 50.33 D) 42.33 E) 69.23 90 100=69.23 130 52) The value of E. / Die waarde van E. A) 110.67 B) 120.67 C) 75.44 D) 84.62 E) 70.67 110 100=84.62 130 53) The value of H. / Die waarde van H. A) 134.69 B) 103.37 C) 145.63 D) 116.67 E) 100 D E F G H I 130 100=100 130 54) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is ________ minutes. A) 80 B) 64 C) 1600 D) 40 Since X ==80 . 55) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling distribution of the sample mean is ________ minutes. A) 40 B) 5 C) 1600 D) 0.625 Since X= 40 = =5 . n 64 56) A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is ________. A) 0.2444 B) 0.7566 C) 0.3446 D) 0.6554 57) A manufacturer