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Statistics And Probability With Applications For Engineers And Scientists Using MINITAB R And JMP 2nd Edition Irwin Guttman, Kalanka P. Jayalath, Bhisham C. Gupta - Solutions
7. There are four roads connecting location A and location B. The probabilities that if a person takes Road I, Road II, Road III, or Road IV from location A to B, then he/she will arrive late because of getting stuck in the traffic are 0.3, 0.20, 0.60, and 0.35, respectively. Suppose that a person
6. An industry uses three methods, M1,M2, and M3 to manufacture a part. Of all the parts manufactured, 45% are produced by method M1, 32% by method M2, and the rest 23% by method M3. Further it has been noted that 3% of the parts manufactured by method M1 are defective, while 2% manufactured by
5. Suppose that a random experiment consists of randomly selecting one of four coins C1, C2, C3, and C4, tossing it and observing whether a head or a tail occurs. Further suppose that the coins C1, C2, and C3 are biased such that the probabilities of a head occurring for coins C1, C2, and C3 are
4. Suppose that four attorneys A1,A2,A3, and A4 deal with all the criminal cases in a district court. The following table gives the percentages of the cases that each of these attorneys handles, and also the probability that each loses the case;Attorney Probability of handling the case Probability
3. Suppose that A1,A2,A3,A4, and A5 are five mutually exclusive and exhaustive events in a sample space S, and suppose that P(A1) = 0.2, P(A2) = 0.1, P(A3) =0.15, P(A4) = 0.3, and P(A5) = 0.25. Another event E in S is such that P(E|A1) =0.2, P(E|A2) = 0.1, P(E|A3) = 0.35, P(E|A4) = 0.3, and P(E|A5)
2. Three balanced coins are tossed simultaneously. What is the probability that exactly two heads appear given that at least one head has appeared?
1. A regular die is rolled. If the number that showed up is odd, what is the probability that it is 3 or 5?
12. Each of 10 websites either contains (C) an ad of a car manufacturer or does not contain the ad (N). How many sample points are there in the sample space of a random experiment that selects a website at random?
11. In a random experiment, one die is rolled, one coin is tossed, and a card is drawn from a well-shuffled regular deck of playing cards and its suit noted. How many sample points are there in the sample space of this random experiment?
10. How many different car plates can be issued if the Department of Motor Vehicles decides to first use two letters of the English alphabet and then any four of the digits 0, 1, 2, . . . , 9?
9. A cholesterol-lowering drug is manufactured by four different pharmaceutical companies in five different strengths and two different forms (tablet and capsule).In how many different ways can a physician prescribe this drug to a patient?
8. How many different permutations can be obtained by arranging the letters of the word engineering? Cardiologist?
7. If 13 cards are dealt from a thoroughly shuffled deck of 52 ordinary playing cards, find the probability of getting five spades and four diamonds.
6. If in Problem 3 above, the committee consists of just four members, then in how many ways can the class select the committee?
5. A chain restaurant offers a dinner menu with four different soups, three different salads, 10 entrees, and four desserts. In how many ways can a customer choose a soup, a salad, an entr´ee, and a dessert?
4. A multiple-choice board exam consists of 15 questions, each question having four possible answers. In how many different ways can a candidate select one answer to each question?
3. In how many ways can a class of 30 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary (a) if any student may serve either of these roles but no student may serve in multiple roles and (b) if any student may serve in multiple
2. A small motel with nine rooms has three twin beds in two rooms, two twin beds in three rooms, and one twin bed in rest of the four rooms. In how many different ways can the manager of the motel assign these rooms to a group of 16 guests who told the manager that they have no preference about
1. In a certain clinical trial, a medical team wants to study four different doses of a new medication for cervical cancer in five patients. In how many different ways can the team select one dose of the medication and one of the patients?3.5 Conditional Probability 113
14. Two dice are rolled and the sum of the points that appear on the uppermost faces of the two dice is noted. Write all possible outcomes such that:(a) The sum is seven.(b) The sum is five or less.(c) The sum is even or nine.Find the probability for the occurrence of each event you described in
(a) At least two heads occur.(b) At most one head occurs.(c) Exactly two heads occur.(d) No head occurs.Find the probability for the occurrence of each event.
12. The time a biology major takes to dissect a frog is recorded to the nearest minute.Describe the sample space for this random experiment.13. Three coins are tossed. Describe the following events:
11. Five women are selected randomly, and their mammograms are examined. Each mammogram is classified as indicating that the woman has breast cancer (C) or does not have breast cancer (N). Write the sample space for this random experiment.
10. In a random experiment four “lock nuts” are selected and each nut is classified either as defective (D) or nondefective (N). Write the sample space for this random experiment.
9. Suppose that a person is taken to an ER and that A is the event that he is diagnosed with liver cancer, B is the event that he will need a liver transplant, and C is the event that the hospital will find a matching liver on time. The Venn diagram representing these events and various other
8. Given a sample space S = {x|3 < x < 10} and two events A and B in S defined as A = {x|4 < x < 7} and B = {x|5 < x < 9}, describe the following events:(a) A¯, (b) A ∪ B, (c) A ∪ B (d) A ∩ B
7. Given a sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9} and four events A,B,C, and D in S that are defined as A = {1, 3, 4, 7}, B = {2, 4, 6, 8, 9}, C = {1, 4, 5, 7}, and D ={1, 3, 5, 7, 9}, describe the following events:(a) A ∩ B ∩ C, (b) (A ∩ B) ∪ (C ∩ D), (c) A ∩ (B ∪ C ∪ D), (d)
6. A box contains a shipment of n(n > 4) computer chips, of which four are defective.Four chips are randomly selected and examined as to whether or not the chips are defective. Describe the sample space for this experiment. What is the probability that(a) Exactly one of the four chips is
5. Three students are randomly selected from a freshmen engineering class, and it is observed whether they are majoring in chemical, mechanical, or electrical engineering.Describe the sample space for this experiment. What is the probability that at most one of the three students is an EE major?
4. Two regular dice are rolled simultaneously. If the numbers showing up are different, what is the probability of getting a total of 10 points?
3. Describe the sample space for each of the following experiments:(a) Three coins are tossed.(b) One die is rolled and a coin is tossed.(c) Two dice are rolled.(d) A family has three children of different ages, and we are interested in recording the gender of these children such that the oldest
2. Draw a Venn diagram for each event described in Problem 1 above.
1. Consider a sample space S. Let A and B be any two events in S. Write the expressions in terms of unions, interactions, and complements for the following events:(a) At least one of the events A or B occurs.(b) Both events A and B occur.(c) Neither A nor B occurs.(d) Exactly one of the events A or
45. It is generally believed that students’ performance on a test is related to number of hours of sleep they have the night before the test. To verify this belief, 12 students were asked how many hours they slept on the night before the test. The following data shows the number of hours of sleep
44. The following data gives the heights (in.) and weights (lb) of eight individuals. Determine the correlation coefficient between the heights and weights. Interpret the value of the correlation coefficient you have determined.Individuals 1 2 3 4 5 6 7 8 Heights 77 72 73 76 72 73 77 72 Weights 156
43. The following data gives the inflation rate and interest rates in the United States over 10 consecutive periods. Determine the correlation coefficient between the inflation rate and the interest rates in the United States. Interpret the value of the correlation coefficient you determined.Period
42. The following data give the number of flights that left late at a large airport over the past 30 days:50 59 63 30 120 55 49 47 43 51 47 51 57 62 58 50 39 53 50 45 43 46 52 59 48 36 51 33 42 32(a) Prepare a complete frequency distribution table for these data.(b) Prepare a box plot for these
41. The following two data sets give the number of defective ball bearings found in 20 boxes randomly selected from two shipments:Shipment I 60 65 79 71 67 68 73 56 59 63 66 59 72 77 79 69 71 70 60 55 ShipmentII 45 55 56 50 59 60 48 38 42 41 37 57 55 49 43 39 45 51 53 55(a) Find the quartiles for
40. The following data give the test scores of 40 students in a statistics class:68 78 92 80 87 79 74 85 86 88 91 97 71 72 81 86 60 40 76 77 20 99 80 79 89 87 87 80 83 95 92 98 87 86 95 96 76 75 79 80(a) Find the sample mean ¯X and the sample standard deviation S for these data.(b) Prepare a
39. Prepare box plots for the data in Problems 37 and 38. Comment on the shape of the distribution of these two data sets.Review Practice Problems 95
38. The owner of the facility in Problem 37 has another plant where the shipments received are much larger than at the first plant. The quality engineer at this facility also decides to collect the data on defectives received in each shipment. The last 15 shipments provided the following data:21 30
37. The following data give the number of defective parts received in the last 15 shipments at a manufacturing plant:8 10 12 11 13 9 15 14 10 16 18 12 14 16 13(a) Find the mean of these data.(b) Find the standard deviation of these data.(c) Find the coefficient of variation for these data.
36. Assume that the data in Problem 35 come from a population having a bell-shaped probability distribution. Then, using the empirical rule, determine how many data values one would expect to fall within the intervals ¯X ± 2S and ¯X ± 3S. Compare your results with the actual number of data
35. The following sample data give the GRE scores (actual score—2000) of 20 students who have recently applied for admission to the graduate program in an engineering school of a top-rated US university:268 320 290 310 300 270 250 268 330 290 240 269 295 325 316 320 299 286 269 250(a) Find the
34. The following sample data give the number of pizzas sold by a Pizza Hut over a period of 15 days:75 45 80 90 85 90 92 86 95 95 90 86 94 99 78(a) Prepare a box plot for these data and comment on the shape of this data set.(b) Find the mean, median, and standard deviation of these data.
33. Suppose that the manager of a pulp and paper company is interested in investigating how many trees are cut daily by one of its contractors. After some investigation, the manager finds that the number of trees cut daily by that contractor forms a bell shaped distribution with mean 90 and
32. A data set has a mean of 120 and a standard deviation of 10. Using the empirical rule, find what percentage of data values fall:(a) Between 110 and 130.(b) Between 100 and 140.(c) Between 90 and 150.
31. The following data give the yearly suggested budget (in dollars) for undergraduate books by 20 randomly selected schools from the whole United States:690 650 800 750 675 725 700 690 650 900 850 825 910 780 860 780 850 870 750 875(a) Find the mean and the standard deviation for these data.(b)
30. The following data give the time (in minutes) taken by 20 students to complete a class test:55 63 70 58 62 71 50 70 60 65 59 62 66 71 58 70 75 70 65 68(a) Find the mean, median, and mode for these data.(b) Use values of the mean, median, and mode to comment on the shape of the frequency
29. The following data give the overtime wages (in dollars) earned on a particular day by a group of 40 randomly selected employees of a large manufacturing company:30 35 45 50 25 30 36 38 42 40 46 36 30 35 24 46 42 50 40 40 35 34 34 30 28 32 30 26 28 36 40 42 40 38 38 36 45 40 36 42(a) Find the
28. The following data give the test scores of 57 students in an introductory statistics class:68 78 92 80 87 79 74 85 86 88 91 97 71 72 81 86 60 40 76 77 20 99 80 79 89 87 87 80 83 95 92 98 87 86 95 96 75 76 79 80 85 81 77 76 84 82 83 56 68 69 91 88 69 75 74 59 61(a) Find the values of three
27. Refer to the data in Problem 26. Determine the following:(a) The values of the three quartiles Q1,Q2, and Q3.(b) The IQR for these data.(c) Construct a box-plot for these data and verify if the data contains any outliers.
26. A car manufacturer wants to achieve 35 miles/gal on a particular model. The following data give the gas mileage (rounded to the nearest mile) on 40 randomly selected brand-new cars of that model. Each car uses regular unleaded gasoline:34 33 36 32 33 34 35 37 32 33 32 31 34 37 32 33 33 36 34 31
25. Compute ¯X, S2, and S for the data in Problem 24. Then,(a) Find the number of data points that fall in the intervals ¯X ± S, ¯X ± 2S, and¯X± 3S(b) Verify whether the empirical rule holds for these data.
24. The following data give lengths (in mm) of a type of rods used in car engines.128 118 120 124 135 130 128 116 122 120 118 125 127 123 126 124 120 132 131 119 117 124 129 131 133 115 121 122 127 127 134 128 132 135 125 120 121 126 124 123(a) Determine the quartiles (Q1,Q2,Q3) for this data.(b)
23. Prepare a frequency table for the data in Problem 9 of Section 2.4. Find the mean and the variance for the grouped and the ungrouped data. Then compare the values of the mean and variance of the grouped and the ungrouped data.
22. The following data give the number of physicians who work in a hospital and are classified according to their age:Age [35–40) [40–45) [45–50) [50–55) [55–60) [60–65]Frequency 60 75 68 72 90 55 Find the mean and the standard deviation for this set of grouped data.92 2 Describing Data
21. Collect the closing price of two stocks over a period of 10 sessions. Calculate the coefficients of variation for the two data sets and then check which stock is more risky.
20. The owner of the gas station of Problem 19 also owns another gas station. He decided to collect similar data for the second gas station during the same period. These data are given below.570 590 600 585 567 570 575 580 577 583 589 585 595 570 574 576 581 583 595 591 585 583 580 597 599 600 577
19. The following data give daily sales (in gallons) of gasoline at a gas station during April:414 450 380 360 470 400 411 465 390 384 398 412 416 454 459 395 430 439 449 453 464 450 380 398 410 399 416 426 430 425(a) Find the mean, median, and mode for these data. Comment on whether these data are
18. The following data give hourly wages of 20 workers randomly selected from a chipmaker company:16 12 18 15 23 29 21 20 21 25 18 27 21 25 22 16 24 26 21 26 Determine the mean, median, and mode for these data. Comment on whether these data are symmetric or skewed.Review Practice Problems 91
17. Find the mean, median, and mode for the following sample data on credit hours for which students are registered in a given semester:7 11 8 12 7 6 14 17 15 13
16. A group of dental professionals collected some data on dental health and concluded that 10% of the Americans have zero or one cavity, 50% have two or three cavities, 30% have four cavities, and rest of the 10% have five or more cavities. Construct a pie chart that describes the dental health of
15. We know that from a grouped data set we cannot retrieve the original data. Generate a new (hypothetical) data set from the frequency distribution table that you prepared in Problem 14. Reconstruct a frequency distribution table for the new set and comment on whether the two frequency tables
14. The following data give the total cholesterol levels (mg/100 mL) of 100 US males between 35 to 65 years of age:177 196 150 167 175 162 195 200 167 170 179 172 176 179 177 153 177 189 185 167 151 177 191 177 175 151 173 199 167 197 188 163 174 151 183 174 177 200 182 195 160 151 177 154 150 180
13. The following data give the number of cars owned by 50 randomly selected families in a metropolitan area:3 5 2 1 2 4 3 1 2 3 4 2 3 2 5 3 1 2 4 3 2 1 2 1 4 5 1 2 3 2 3 4 2 3 1 2 3 2 4 2 3 2 1 3 1 2 4 2 3 2(a) Construct a single-valued frequency distribution table for these data.(b) Compute the
12. The following data give the salaries (in thousands of dollars) of 62 randomly selected engineers from different manufacturing companies located in different regions of the United States:65 45 85 68 98 95 58 62 64 54 57 58 85 120 45 56 150 140 123 65 55 66 76 88 45 50 60 66 55 46 48 98 56 66 185
11. To improve the quality of a crucial part used in fighter jets, a quality control engineer is interested in finding the type of defects usually found in that part. He labels these defects as A, B, C, D, and E based on severity of the defect. The following data show the type of defects found in
10. The following data give the number of employees from 19 different sectors of a large company who were absent for at least two days from a certain training program:7 5 10 12 6 7 8 10 3 16 10 9 8 10 7 6 9 11 2 Construct a dot plot for these data and comment on what you observe in these data.
9. Consider the following stem-and-leaf diagram:Stem Leaf 3 257 4 0 3 6 8 9 5 1 2 2 7 8 6 3 5 6 6 9 9 7 1 5 5 7 8 Reproduce the data set represented by the diagram.Review Practice Problems 89
8. The following data give the number of defective parts produced in 21 consecutive shifts of 1 wk 15 14 18 16 17 13 27 14 15 10 30 14 8 14 15 17 15 13 14 16 20(a) Prepare a line graph of these data.(b) Check if any peaks or dips appear in the line graph.(c) As a quality manager of the company,
7. Suppose that in a midwestern state, a legislator running for governor proposes the following state budget (in millions of dollars) for the following year:Education 900 Medicaid 400 Other social programs 500 Road and bridges 350 Agriculture 400 Others 250 Use JMP, MINITAB, or R to do the
6. Refer to the data in Problem 15 of Section 2.4.(a) Construct a frequency histogram for these data.(b) Construct a relative-frequency histogram for these data.
5. Suppose there are two fund-raising concerts at a university. The following data give the number of students by their class standing who attended one or the other of the concerts:Class standing Frequency-1 Frequency-1 Freshmen 16 40 Sophomore 18 30 Junior 20 21 Senior 15 20 Graduate 30 15 88 2
4. The following data classify a group of students who are attending a seminar on environmental issues by their class standing:Class standing Frequency Freshmen 16 Sophomore 18 Junior 20 Senior 15 Graduate 30(a) Construct a bar chart for these data.(b) Construct a pie chart for these data.
3. The following data give the number of machines in a shoe factory that had breakdowns during the past 21 shifts:3, 2, 1, 0, 2, 1, 4, 2, 0, 1, 2, 3, 1, 0, 4, 2, 1, 10, 2, 1, 2 Construct a dot plot for these data. If you were the maintenance engineer, what would you learn from these data?
2. A saving and loan institution wants to find how many of their customers default their loan payments. The following data give the number of customers who did not make their payment on time at least once over the past 12 months:15, 20, 18, 16, 3, 19, 14, 17, 17, 16, 30, 15 Construct a dot plot for
1. During a flu season, it is common that many workers cannot come to work because either they themselves are sick or they have to take care of their sick children. The following data give the number of employees of a company who did not come to work on 18 days during a flu season:7, 5, 10, 12, 6,
2. Is the value of correlation coefficient consistent with what you concluded in part (a)?
4. The following scores give two managers’ assessments of ten applicants for the position of a senior engineer:Manager1 7 8 9 7 9 8 9 7 9 6 Manager2 8 6 9 9 8 7 9 8 7 8(a) Construct a scatter plot for these data. By observing this scatter plot, do you expect the correlation between assessments of
3. The following data show the experience (in years) and yearly salaries (in thousands of dollars) of 10 engineers:Experience 10 12 8 15 6 11 14 16 15 12 Salaries 98 95 97 110 88 102 120 128 105 104(a) Construct a scatter plot for these data. By observing this scatter plot, do you expect the
2. The following data give the final exam scores in biology and chemistry of eight science majors:Biology scores 85 88 78 92 89 83 79 95 Chemistryscores 90 84 86 95 94 89 84 87 84 2 Describing Data Graphically and Numerically(a) Draw a scatter plot for these data. By observing this scatter plot, do
1. The following data give the heights (cm) and weights (lb) of 10 male undergraduate students:Heights 170 167 172 171 165 170 168 172 175 172 Weights 182 172 179 172 174 179 188 168 185 169(a) Draw a scatter plot for these data. By observing this scatter plot, do you expect the correlation between
7. Reconsider the data in Problem 5 of Section 2.6 and do the following:(a) Find the mean, variance, and standard deviation of these data.(b) Find the three quartiles and the IQR for these data.(c) Prepare a box plot for these data and determine if there are any outliers present in these data.
6. Reconsider the data in Problem 4 of Section 2.6, and do the following:(a) Find the mean, variance, and standard deviation of these data.(b) Find the three quartiles and the IQR for these data.(c) Prepare a box plot for these data and determine if there are any outliers present in these data.
5. Consider the following two sets of data:Set I 29 24 25 26 23 24 29 29 24 28 23 27 26 21 20 25 24 30 28 28 29 28 22 26 30 21 26 27 25 23 Set II 46 48 60 43 57 47 42 57 58 59 52 53 41 58 43 50 49 56 57 54 51 46 60 44 55 43 60 50 51 54 50 43 44 53 51 58(a) Find the mean and standard deviation for
4. The following data provide the number of six sigma black belt Engineers in 36 randomly selected manufacturing companies in the United States:73 64 80 67 73 78 66 78 59 79 74 75 73 66 63 62 61 58 65 76 60 79 62 63 71 75 56 78 73 75 63 66 71 74 64 43(a) Find the 60th percentile of these data.(b)
3. The following data give the physics lab scores of 24 randomly selected of physics majors:21 18 21 18 20 18 18 59 19 20 20 20 19 18 21 58 19 22 19 18 22 18 22 56 Construct a box plot for these data and examine whether this data set contains any outliers.80 2 Describing Data Graphically and
2. The following data gives the reaction time (in minutes) of a chemical experiment conducted by 36 chemistry majors:55 58 46 58 49 46 41 60 59 41 59 42 40 44 42 58 46 58 58 40 51 59 48 46 42 43 56 48 41 54 56 57 48 43 49 43(a) Find the mean, mode, and median for these data.(b) Prepare a box plot
5. The data below gives the time (in minutes) taken by 36 technicians to complete a small project:55 58 46 58 49 46 41 60 59 41 59 43 42 40 44 42 58 46 58 58 40 51 59 49 48 46 42 43 56 48 41 54 56 57 48 43 Construct a frequency distribution table for these data. Find the mean and the standard
4. The following data give the systolic blood pressures of 30 US male adults whose ages are 30–40 years old:113 122 111 119 125 113 123 122 115 115 112 117 121 116 118 116 109 109 112 116 122 109 110 115 109 115 120 122 125 111(a) Determine the mean, median, and mode of these data.(b) Determine
3. Use the frequency distribution table you prepared in Problem 6 of Section 2.3 to do the following:(a) Determine the mean, median, and mode of the grouped data.(b) Determine the variance and the standard deviation of the grouped data.
2. Use the frequency distribution table you prepared in Problem 5 of Section 2.3, to do the following:(a) Determine the mean, median, and mode of the grouped data.(b) Determine the variance and the standard deviation of the grouped data.
1. Use the frequency distribution table you prepared in Problem 4 of Section 2.3 to do the following:(a) Determine the mean, median, and mode of the grouped data.(b) Determine the variance and the standard deviation of the grouped data.70 2 Describing Data Graphically and Numerically
11. Consider the following data giving the lengths (to the nearest centimeter) of a part used in the fuselage of a plane:24 22 23 25 22 21 23 24 20 22 22 24 21 23 23 20 22 24 23 25(a) Determine the mean (¯X ) and the standard deviation (S) of these data.(b) Calculate the intervals (¯X ± S), (¯X
10. According to Chebyshev’s inequality, what we can say about the lower limit of the percentage of any set of data values that must lie within k standard deviations of the mean when (a) k = 3, (b) k = 3.5, (c) k = 4, (d) k = 5?
9. The average salary of engineers in a manufacturing company is $55,600 with a standard deviation of $4500. Assuming that the shape of the distribution of salaries is bell-shaped, estimate the ranges of salaries within which approximately 68% and 95% of all the engineers’ salaries are expected
8. The following data shows the tread depth in millimeters (mm) of 20 of tires selected randomly from a large shipment received by a dealer:6.28 7.06 6.50 6.76 6.82 6.92 6.86 7.15 6.57 6.48 6.64 6.94 6.49 7.14 7.16 7.10 7.08 6.48 6.40 6.54(a) Find the mean and the median for these data.(b) Find the
7. John is a very hard-working and an ambitious student. In a certain semester, he took in fact six courses that had 5, 4, 4, 3, 3, and 2 credit hours. The grade points he earned in these courses at the end of the semester were 3.7, 4.0, 3.3, 4.0, 3.7, and 4.0, respectively. Find his GPA for that
6. Use the values of the mean (¯X ) and the standard deviation (S) found in part (a) of Problem 5 above to determine the number of data points that fall in the intervals,(¯X − S, ¯X + S), (¯X − 2S, ¯X + 2S), and (¯X − 3S, ¯X + 3S). Assuming that the distribution of this data set is
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