New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
introduction to probability statistics
Introduction To Probability And Statistics 3rd Edition William Mendenhall - Solutions
6.32 Tennis Anyone? A stringer of tennis rack- ets has found that the actual string tension achieved for any individual racket stringing will vary as much as 3 kilograms per square centimetre (km/ cm) from the desired tension set on the stringing machine. If the stringer wishes to string at a
6.33 Sunday Shopping When Nova Scotia lifted its Sunday shopping ban, retail stores of all kinds could finally open on Sundays and other holidays, the only exception being Remembrance Day. Nova Scotia was one of the last provinces to place Sunday restrictions on retailers. Suppose that the amount
6.34 Pulse Rates Your pulse rate is a measure of the number of heartbeats per minute. It can be measured in several places on your body, where an artery passes close to the skin. Once you find the pulse, count the number of beats per minute, or, count for 30 seconds and multiply by two. What's a
6.43 Consider a binomial experiment with n = 20 and p=0.4. Calculate P(X= 10) using each of these methods:a. Table 1 in Appendix Ib. The normal approximation to the binomial probabil- ity distribution
6.42 Refer to Exercise 6.41. Use the normal approxi- mation to calculate P(X = 5) and P(X7). Compare with the exact values obtained from Table 1 in Appendix I.
6.41 Suppose the random variable X has a binomial distribution corresponding to n = 20 and p = 0.30. Use Table 1 of Appendix I to calculate these probabilities:a. P(X=5)b. P(X7)
6.40 Let X be a binomial random variable for n=25, p=0.2.a. Use Table 1 in Appendix I to calculate P(4 X 6).b. Find and or for the binomial probability distribu- tion, and use the normal distribution to approxi- mate the probability P(4X6). Note that this value is a good approximation to the exact
6.39 Let X be a binomial random variable with n = 100 and p = 0.2. Find approximations to these probabilities: a. P(X>22) b. P(X22) c. P(20
6.36 Consider a binomial random variable X with n=45 and p=0.05.a. Are np and ng both larger than 5?b. Based on your answer to parta, can we use the normal approximation to approximate the binomial probabilities associated with X? If not, is there another possible approximation we could use?
A producer of soft drinks was fairly certain that her brand had a 10% share of the soft drink market. In a market survey involving 2500 consumers of soft drinks, X = 211 expressed a preference for her brand. If the 10% figure is correct, find the probability of observing 211 or fewer consumers who
The reliability of an electrical fuse is the probability that a fuse, chosen at random from production, will function under its designed conditions. A random sample of 1000 fuses was tested and X=27 defectives were observed. Calculate the approximate prob- ability of observing 27 or more
Use the normal curve to approximate the probability that X=8, 9, or 10 for a binomial random variable with n = 25 and p = 0.5. Compare this approximation to the exact binomial probability.
6.19 Human Heights Human heights are one of the many biological random variables that can be modelled by the normal distribution. The average height of Cana- dian women aged 18 and older is 163 centimetres (cm), while the average height for men is 177 cm. Assume the standard deviation for the
6.18 Ground Beef The meat department at a local supermarket specifically prepares its "1-kilogram" packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1 kilogram (kg). Suppose that the weights of these "1-kilogram" packages are normally
6.17 A normal random variable X has an unknown mean and standard deviation. The probability that X exceeds 4 is 0.9772, and the probability that X exceeds 5 is 0.9332. Find and ..
6.1 Consider a standard normal random variable with =0 and standard deviation = 1. Use Table 3 to find the following probabilities:a. P(z
Refer to Example 6.10. In times of scarce energy resources, a competitive advantage is given to an automobile manufacturer who can produce a car that has substantially better fuel economy than the competitors' cars. If a manufacturer wishes to develop a compact car that outperforms 95% of the
Studies show that gasoline use for compact cars sold in North America is normally dis- tributed, with a mean of 100 km per 9 L (km/L) and a standard deviation of 10 km/9 L. What percentage of compacts get 110 km/9 L or more?
Let X be a normally distributed random variable with a mean of 10 and a standard deviation of 2. Find the probability that x lies between 11 and 13.6.
Find the value of z-say zo-such that 0.95 of the area is within zo standard deviations of the mean.
Find the probability that a normally distributed random variable will fall within these ranges: 1. One standard deviation of its mean 2. Two standard deviations of its mean
Find P(-0.5 FIGURE 6.11 Area under the standard normal curve for Example 6.6 f(z) A, 0.3085- -0.5 0 1.0
Find P(z -0.5). This probability corresponds to the area to the right of a point z=-0.5 standard deviation to the left of the mean (see Figure 6.10). FIGURE 6.10 Area under the standard normal curve for Example 6.5 A = 0.3085 Z -0.5 0
Find P(z 1.63). This probability corresponds to the area to the left of a point z=1.63 standard deviations to the right of the mean (see Figure 6.9). FIGURE 6.9 Area under the standard f(z) normal curve for Example 6.4 0.9484 0 1.63 Z
Suppose X has an exponential probability density function with mean . Show that P(Xab Xa) = P(X> b), a > 0, b>0.
The magnitude of most earthquakes is measured on the Richter scale. It was invented by Charles F. Richter in 1934. For example, using this scale, a magnitude 5-5.9 is termed as a moderate earthquake (slight damage to buildings and other structures). Suppose the magnitudes of earthquakes in a region
The waiting time at a Canadian supermarket checkout has an exponential distribution with an average time of five minutes. Thus, the probability density function isThe function is shown in Figure 6.5. f(x) = e x>0. 5
How to Calculate Binomial Probabilities Using the Normal Approximation
6.2 Find these probabilities associated with the standard normal random variable z:a. P(z>5)c. P(z
6.3 Calculate the area under the standard normal curve to the left of these values:a. z=1.6c. z=0.90b. z=1.83d. z=4.18
6.16 A normal random variable X has mean 50 and standard deviation 15. Would it be unusual to observe the value X 0? Explain your answer.
6.15 A normal random variable X has mean 35 and standard deviation 10. Find a value of X that has area 0.01 to its right. This is the 99th percentile of this normal distribution.
6.14 A normal random variable x has an unknown mean and standard deviation or =2. If the probability that X exceeds 7.5 is 0.8023, find .
6.13 A normal random variable x has mean = 1.20 and standard deviation =0.15. Find the probabilities of these X-values:a. 1.00 < X < 1.10 b.X > 1.38c. 1.35 < X < 1.50
6.12 A normal random variable x has mean = 10 and standard deviation = 2. Find the probabilities of these X-values:a. X> 13.5b. X
6.11 Find the following percentiles for the standard normal random variable z:a. 90th percentilec. 98th percentileb. 95th percentiled. 99th percentile
6.10a. Find a zo such that P(-z
6.9a. Find a zo that has area 0.9505 to its leftb. Find a zo that has area 0.05 to its left
6.5 Find the following probabilities for the standard normal random variable z: a. P(-1.43
6.8 Find a zo such that P(-z
6.7a. Find a zo such that P(z> zo) = 0.025.b. Find a zo such that P(z < zo )=0.9251
6.6 Find these probabilities for the standard normal random variable z: a. P(z 1.96) b. P(z < 1.645) d. P(-2.58 <
6.4 Calculate the area under the standard normal curve between these values:a. z=-1.4 and z=1.4b. z=-3.0 and z=3.0
How to Use Table 3 to Calculate Probabilities under the Standard Normal Curve
In 2006-2007, the Canadian in-hospital preterm birth (prematurity, that is, birth before 37 weeks of gestation) and SGA (small for their gestational age) rates were approximately 8.1% and 8.3%, respectively, accounting for more than 54,000 live births combined. Among the provinces, Alberta and
6.85 Snacking and TV Is television dangerous to your diet? Psychologists believe that excessive eating may be associated with emotional states (being upset or bored) and environmental cues (watching television, reading, and so on). To test this theory, suppose you randomly selected 60 overweight
6.84 Suppliers A or B? A purchaser of electric relays buys from two suppliers, A and B. Supplier A supplies two of every three relays used by the com- pany. If 75 relays are selected at random from those in use by the company, find the probability that at most 48 of these relays come from supplier
6.83 Plant Genetics In Exercise 5.76, a cross between two peony plants-one with red petals and one with streaky petals-produced offspring plants with red petals 75% of the time. Suppose that 100 seeds from this cross were collected and germinated, and x, the number of plants with red petals, was
6.82 Long Distance It is known that 30% of all calls coming into a telephone exchange are long-distance calls. If 200 calls come into the exchange, what is the probability that at least 50 will be long-distance calls?
6.81 No Shows, again An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. If the airline sells 160 tickets for a flight that has only 155 seats, what is the probability that a seat will be available for every per- son holding a reservation
6.80 The First-Year Class The admissions office of a small university is asked to accept deposits from a number of qualified prospective first-year students so that, with probability about 0.95, the size of the first year class will be less than or equal to 120. Suppose the applicants constitute a
6.79 Light Bulbs A manufacturing plant uses 3000 electric light bulbs whose life spans are normally distributed, with mean and standard deviation equal to 500 and 50 hours, respectively. In order to minimize the number of bulbs that burn out during operating hours, all the bulbs are replaced after
6.78 Filling Pop Cups A pop machine can be regu- lated to discharge an average of millilitres per cup. If the millilitres of fill are normally distributed, with stan- dard deviation equal to 10 mL, give the setting for uso that 250 mL cups will overflow only 1% of the time.
6.77 Forecasting Earnings A researcher notes that senior corporation executives are not very accurate forecasters of their own annual earnings. He states that his studies of a large number of company executive forecasts "showed that the average estimate missed the mark by 15%."a. Suppose the
6.76 TV Viewers An advertising agency has stated that 20% of all television viewers watch a particular program. In a random sample of 1000 viewers, x=184 viewers, were watching the program. Do these data present sufficient evidence to contradict the adver- tiser's claim?
6.75 Servicing Automobiles The length of time required for the periodic maintenance of an automo- bile will usually have a probability distribution that is mound-shaped and, because some long service times will occur occasionally, is skewed to the right. The length of time required to run a
6.74 How Long Is the Test? The average length of time required to complete a college achievement test was found to equal 70 minutes, with a standard devia- tion of 12 minutes. When should the test be terminated if you wish to allow sufficient time for 90% of the students to complete the test?
6.73 Garage Door Openers Most users of auto- matic garage door openers activate their openers at distances that are normally distributed, with a mean of 10 m and a standard deviation of 2.7 m. To minimize interference with other remote-controlled devices, the manufacturer is required to limit the
6.86 Gestation Times The Biology Data Book reports that the gestation time for human babies averages 278 days with a standard deviation of 12 days. Suppose that these gestation times are normally distributed.a. Find the upper and lower quartiles for the gestation times.b. Would it be unusual to
6.87 Tax Audits In Exercise 6.28 we suggested that the Canada Revenue Agency assign auditing rates per province by randomly selecting 50 auditing percent- ages from a normal distribution with a mean equal to 1.55% and a standard deviation of 0.45%.a. What is the probability that a particular
Moderate prematurity refers to babies who are born between 28 and 32 completed weeks gestational age with a birth weight range between 1000 and 1500 grams. The length of time a baby has spent in the womb, or more specifically the number of completed weeks of pregnancy, is called the gestational
Moderate prematurity refers to babies who are born between 28 and 32 completed weeks gestational age with a birth weight range between 1000 and 1500 grams. The length of time a baby has spent in the womb, or more specifically the number of completed weeks of pregnancy, is called the gestational
4. If you had a score of 92 on the exam and you had the choice of curving the grades or using the absolute standard of 90-100 for an A, 80-89 for a B, 70-79 for a C, and so on, what would be your choice? Explain your reasoning. Is the skewness of the distribution of grades a problem?Very often, at
3. Find the cutoff points for A, B, C, D, and F grades corresponding to these rounded values.Very often, at the end of an exam that seemed particularly difficult, students will ask the professor, "Are you going to curve the grades?" Unfortunately, "curving the grades" doesn't necessarily mean that
2. How many standard deviations on either side of the mean will be the cutoff points for the B and D grades? A histogram of the grades for an introductory statistics class together with sum- mary statistics follows.For ease of calculation, round the number of standard deviations for C grades to 0.5
1. If the average C grade is centred on the average grade for all students, and if we assume that the grades are normally distributed, how many standard deviations on each side of the mean will designate the C grades?Very often, at the end of an exam that seemed particularly difficult, students
6.94 Transplanting Cells Briggs and King devel- oped the technique of nuclear transplantation, in which the nucleus of a cell from one of the later stages of the development of an embryo is transplanted into a zygote (a single-cell fertilized egg) to see whether the nucleus can support normal
6.93 Faculty Salaries Several years ago, OCUFA President Michael Piva wrote a very helpful explana- tion of university salary structures, the nature of career development increments, and the problems created when they are mistaken for or misrepresented as "raises." A 1988 study by Hal Management
6.92 Test Scores The scores on a national achieve- ment test were approximately normally distributed, with a mean of 540 and a standard deviation of 110.a. If you achieved a score of 680, how far, in standard deviations, did your score depart from the mean?b. What percentage of those who took the
6.91 Stamps Philatelists (stamp collectors) often buy stamps at or near retail prices, but, when they sell, the price is considerably lower. For example, it may be reasonable to assume that (depending on the mix of a collection, condition, demand, eco- nomic conditions, etc.) a collection will sell
6.90 Normal Temperatures In Exercise 1.68, Allen Shoemaker derived a distribution of human body temperatures, which has a distinct mound-shape. Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 37.1 C and a standard deviation of 0.2 degrees.a. If a
6.89 Introvert or Extrovert? A psychological introvert-extrovert test produced scores that had a normal distribution with a mean and standard devia- tion of 75 and 12, respectively. If we wish to designate the highest 15% as extroverts, what would be the proper score to choose as the cutoff point?
6.88 Your Favourite Sport There is a difference in sports preferences between men and women, accord- ing to a recent survey. Among the 10 most popular sports, men include competition-type sports-pool and billiards, basketball, and softball-whereas women include aerobics, running, hiking, and
6.72 Washers The life span of a type of automatic washer is approximately normally distributed, with mean and standard deviation equal to 3.1 and 1.2 years, respectively. If this type of washer is guaranteed for 1 year, what fraction of original sales will require replacement?
6.71 Restaurant Sales The daily sales total (excepting Saturday) at a small restaurant has a prob- ability distribution that is approximately normal, with a mean equal to $1230 per day and a standard devia- tion or equal to $120.a. What is the probability that the sales will exceed $1400 for a
6.45 Same-Sex Marriage in Argentines Same- sex marriage is legal in the Netherlands, Belgium, Spain, Canada, and South Africa, and at least 18 coun- tries offer some form of legal recognition to same-sex unions. Many residents of Argentina's capital have no issue with same-sex couples getting
6.56 Find the following probabilities for the standard normal random variable z: a. P(-1.96 z1.96) b. P(z > 1.96) c. P(z
6.55 Calculate the area under the standard normal curve between these values:a. z=-2.0 and z=2.00b. z=-2.3 and z=-1.5
6.54 Calculate the area under the standard normal curve to the left of these values:a. z=-0.90b. z=2.34c. z=5.4
Suppose that the average birth weights of babies born at hospitals owned by a major health maintenance organization (HMO) are approximately normal with mean 6.75 pounds and standard deviation 0.54 pounds. What proportion of babies born at these hospitals weigh between 6 and 7 pounds? Find the 95th
For a standard normal random variable z, find P(1.2 1. Name columns A and B of a spreadsheet as "20", and "P(z 2. Enter the location of first value of zo (cell A2) into the first box and the word TRUE into the second box. The resulting probability is marked as "Formula result =0.8849" at the bottom
6.53 Trying to be More Frugal? continued Assume that the percentage (37%) is correct for all Canadians, and that a random sample 100 Canadians is selected.a. What is the average number of Canadians who felt they will have to cut back on spending?b. What is the standard deviation of Canadians who
6.52 Trying to Be More Frugal? Many Canadians fear they are spending too much and will have to cut back. Interestingly, 47% of British Columbians-the highest percentage in Canada-think they will have to cut back on spending to maintain their current lifestyle in 10 years, a survey shows. While 37%
6.51 Pepsi's Market Share Two of the biggest soft drink rivals, Pepsi and Coke, are very concerned about their market shares. The pie chart that follows claims that PepsiCo's share of the beverage market is 25%.5 Assume that this proportion will be close to the prob- ability that a person selected
6.50 The Rh Factor In a certain population, 15% of the people have Rh-negative blood. A blood bank serving this population receives 92 blood donors on a particular day.a. What is the probability that 10 or fewer are Rh-negative?b. What is the probability that 15 to 20 (inclusive) of the donors are
6.49 Death Penalty in Lima An overwhelming majority of adults in Peru's capital believe capital punishment would be suitable in specific circum- stances, according to a poll by Apoyo published in El Comercio. In Lima, 81% of respondents would allow the death penalty for people convicted of raping
6.48 Lung Cancer Compilation of large masses of data on lung cancer shows that approximately 1 of every 40 adults acquires the disease. Workers in a certain occupation are known to work in an air-polluted environment that may cause an increased rate of lung cancer. A random sample of n = 400
6.47 No Shows Airlines and hotels often grant reservations in excess of capacity to minimize losses due to no-shows. Suppose the records of a hotel show that, on the average, 10% of their prospective guests will not claim their reservations. If the hotel accepts 215 reservations and there are only
6.46 Genetic Defects Data collected over a long period of time show that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x=60 children with the defect in a total of 50,000 examined. If the 50,000 children were a random sample from the population
6.57 Find a zo such thata. P(zzo) 0.9750b. P(zzo) 0.3594
6.58 Find a zo such that a. P(-zozzo)=0.95 b. P(-zozzo) = 0.98 c. P(-zozzo) 0.90 d. P(-zozzo)=0.99
6.59 A normal random variable x has mean = 5 and standard deviation =2. Find the probabilities associ- ated with the following intervals: a. 1.2 7.5 c. X0
6.62 Find the following probabilities for the standard normal random variable:a. P(0.3 <
6.70 Used Cars A used-car dealership has found that the length of time before a major repair is required on the cars it sells is normally distributed, with a mean equal to 10 months and a standard deviation of 3 months. If the dealer wants only 5% of the cars to fail before the end of the guarantee
6.69 Bearing Diameters A machine operation pro- duces bearings whose diameters are normally distrib- uted, with mean and standard deviation equal to 1.265 and 0.005, respectively. If specifications require that the bearing diameter equal 1.270 cm 0.101 cm, what fraction of the production will be
6.68 Faculty Ages The influx of new ideas into a university, introduced primarily by new young faculty, is becoming a matter of concern because of the increasing ages of faculty members; that is, the distribution of faculty ages is shifting upward due most likely to a shortage of vacant positions
6.67 Drill Bits It is estimated that the mean life span of oil-drilling bits is 75 hours. Suppose an oil explora- tion company purchases drill bits that have a life span that is approximately normally distributed with a mean equal to 75 hours and a standard deviation equal to 12 hours.a. What
6.66 Find zo such that P(-zo
6.65 Find the probability that z lies between z=-1.48 and z=1.48.
6.64 Find zo such that P(z> zo) = 0.5.
Showing 4700 - 4800
of 7136
First
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
Last
Step by Step Answers
Get 50% OFF
Claim Now
