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Introduction To Probability And Statistics 15th Edition William Mendenhall Iii , Robert Beaver , Barbara Beaver - Solutions

Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 36. u 10 and = 2. Find the probability that x is greater than 13.5.
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 37. u 10 and = 2. Find the probability that x is less than 8.2.
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 38. u 10 and = 2. Find the probability that x is between 9.4 and 10.6.
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 39. u 1.2 and =.15. Find P(1.00 < x
Let z be a standard normal random variable with mean m =0 and standard deviation s =1.Find the value c that satisfies the inequalities 30. P(z
Let z be a standard normal random variable with mean m =0 and standard deviation s =1.Find the value c that satisfies the inequalities 29. P(zc) .025
Let z be a standard normal random variable with mean m =0 and standard deviation s =1. Use Table 3 in Appendix I to find the probabilities 20. Between -1.55 and -.44
Let z be a standard normal random variable with mean m =0 and standard deviation s =1. Use Table 3 in Appendix I to find the probabilities 21. Greater than 1.34
Let z be a standard normal random variable with mean m =0 and standard deviation s =1. Use Table 3 in Appendix I to find the probabilities 22. Less than -4.32
Let z be a standard normal random variable with mean m =0 and standard deviation s =1. Use Table 3 in Appendix I to find the probabilities 23. Between .58 and 1.74
Let z be a standard normal random variable with mean m =0 and standard deviation s =1. Use Table 3 in Appendix I to find the probabilities 24. Between -1.96 and 1.96
Let z be a standard normal random variable with mean m=0 and standard deviation s =1. Find the percentiles 25. 2.10 or the 90th percentile
Let z be a standard normal random variable with mean m=0 and standard deviation s =1. Find the percentiles 26. Zos or the 95th percentile
Let z be a standard normal random variable with mean m=0 and standard deviation s =1. Find the percentiles 27. Z or the 98th percentile
Let z be a standard normal random variable with mean m=0 and standard deviation s =1. Find the percentiles 28. Z or the 99th percentile
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 40. = 1.2 and =.15. Find P(x > 1.38).
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
14. Find m, s 2, and s .Use the probability distribution for the random variable x to answer X 0 1 2 3 4 5 p(x).1 .3 .4 .1 ? .05
2. Total number of points scored in a football game Identify the random variables as either discrete or continuous
An insurance company needs to know how much to charge for a $100,000 policy insuring an event against cancellation due to inclement weather. The probability of inclement weather during the time of the event is assessed as 2 in 100. Once they find C, the cost of the policy to break even, they can
In a lottery conducted to benefit a local charity, 8000 tickets are to be sold at $10 each. The prize is a $24,000 compact car. If you purchase two tickets, what is your expected gain?
A “big-box” store sells a particular laptop, but has only four in stock. The manager wonders what today’s demand for this particular laptop will be. She learns from the marketing department that the probability distribution for x, the daily demand for the laptop, is as shown in the table.
Toss two fair coins and let x equal the number of heads observed. Find the probability distribution for x.
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
The error introduced by rounding an observation to the nearest centimeter has a uniform distribution over the interval from 2.5 to .5. What is the probability that the rounding error is less than .2 in absolute value? f(x) 1.50 1.25 1.00 0.75 0.50 -0.5 -0.2 0 0.2 0.5 Fok
The waiting time at a supermarket checkout counter has an exponential distribution with an average waiting time of 5 minutes. What is the probability that you will have to wait more than 10 minutes at the checkout counter? f(x) 0.20- 0.15 0.10+ 0.05 + 0 5 10 15 20 x
3. Shelf life of a particular drug Identify the random variables as either discrete or continuous
4. Height of the ocean’s tide at a given location Identify the random variables as either discrete or continuous
13. Construct a probability histogram to describe p(x).Use the probability distribution for the random variable x to answer X 0 1 2 3 4 5 p(x).1 .3 .4 .1 ? .05
12. Find p(4).Use the probability distribution for the random variable x to answer X 0 1 2 3 4 5 p(x).1 .3 .4 .1 ? .05
11. Your blood pressure Identify the random variables as either discrete or continuous
10. Number of overdue accounts in a department store at a particular time Identify the random variables as either discrete or continuous
9. Number of deer killed per year in a state wildlife preserve Identify the random variables as either discrete or continuous
8. Tensile breaking strength (in pounds per square inch) of 1-inch-diameter steel cable Identify the random variables as either discrete or continuous
7. Increase in length of life attained by a cancer patient as a result of surgery Identify the random variables as either discrete or continuous
6. Number of aircraft near-collisions in a year Identify the random variables as either discrete or continuous
5. Length of a 2-year-old black bass Identify the random variables as either discrete or continuous
Let x have a uniform distribution on the interval 0 to 10. Find the probabilities 1. P(x< 5)
Let x have a uniform distribution on the interval 0 to 10. Find the probabilities 2. P(3 < x < 7)
Let x have an exponential distribution with l = 0.2. Find the probabilities 14. P(4x6)
Let x have an exponential distribution with l = 0.2. Find the probabilities 15. P(x
Let x have an exponential distribution with l = 0.2. Find the probabilities 16. P(3
17. Waiting Times You arrive at a bus stop to wait for a bus that comes by once every 30 minutes. You don’t know what time the last bus came by. The time x that you wait before the bus arrives is uniformly distributed on the interval from 0 to 30 minutes.a. What is the probability that you will
18. Coating Thickness The thickness in microns (m) of a protective coating applied to a conductor designed to work in corrosive conditions is uniformly distributed on the interval from 25 to 50.a. What is the probability that the thickness of the coating is greater than 45 microns?b. What is the
19. Battery Life The length of life (in days) of an alkaline battery has an exponential distribution with an average life of 1 year, so that l51/365.a. What is the probability that an alkaline battery will fail before 180 days?b. What is the probability that an alkaline battery will last beyond 1
20. Helpline Calls The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 40 minutes so that l51/405.025.a. What is the probability that a call to the helpline lasts less than 5 minutes?b. What is the probability that a call to the
Find P(z#1.63). This probability corresponds to the area to the left of a point z51.63 standard deviations to the right of the mean (see Figure 6.10).
Find P(z$2.5). This probability corresponds to the area to the right of a point z52.5 standard deviation to the left of the mean (see Figure 6.11). A = .3085 -0.5 0
Let x have an exponential distribution with l = 0.2. Find the probabilities 13. P(x >6)
Let x have an exponential distribution with l = 1. Find the probabilities 12. P(2
Let x have a uniform distribution on the interval 0 to 10. Find the probabilities 3. P(x > 8)
Let x have a uniform distribution on the interval 0 to 10. Find the probabilities 4. P(2.5 < x < 8.3)
Suppose x has a uniform distribution on the interval from −1 to 1. Find the probabilities 5. P(x < 0)
Suppose x has a uniform distribution on the interval from −1 to 1. Find the probabilities 6. P(x > .7)
Suppose x has a uniform distribution on the interval from −1 to 1. Find the probabilities 7. P(2.5 < x < .5)
Suppose x has a uniform distribution on the interval from −1 to 1. Find the probabilities 8. P(2.7 < x < .2)
Let x have an exponential distribution with l = 1. Find the probabilities 9. P(x > 1)
Let x have an exponential distribution with l = 1. Find the probabilities 10. P(1
Let x have an exponential distribution with l = 1. Find the probabilities 11. P(x < 1.5)
Find P(2.5#z#1.0). This probability is the area between z52.5 and z51.0, as shown in Figure 6.12. f(z) A = 3085 Ap -0.5 0 1.0
Using Table 1 in Appendix I, find the exact values for the binomial probabilities. Then approximate the probabilities using the normal approximation with the correction for continuity. Compare your answers. 13. P(4x6) when n=25 and p=.2
25. Pepsi or Coke? Two of the biggest soft drink rivals, Pepsi and Coke, are very concerned about their market shares. The pie chart that follows claims that Coke’s share of the beverage market is 36%.11 Assume that this proportion will be close to the probability that a person selected at random
26. Plant Genetics In Exercise 47 (Section 5.2), 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
27. Transplanting Cells Briggs and King developed 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
28. Ready, Set, Relax In a recent survey of American workers, approximately 60% said their employer pressured them to work overtime.12 Assume that the 60%figure is correct and that a random sample of n525 Americans is selected.a. Use Table 1 in Appendix I to find the probability that more than 20
29. Smartphone Shopping According to a USA Today snapshot, a large proportion of American shoppers own smartphones and use them while shopping to take pictures of items (51%), to search for coupons (49%) or to compare prices among retailers (43%)Suppose that a random sample of 50 American shoppers
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 pound. 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, z,1.96). Find the value .025 z with area .025 to its right.1. Name columns C1 and C2 of a MINITAB worksheet as “x,” and “P(X,5x),” respectively.Then enter the two values for x (1.2 and 1.96) in the first two cells of column C1.To generate
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 pound. What proportion of babies born at these hospitals weigh between 6 and 7 pounds? Find the 95th
1. Failure Times The time until failure for an electronic switch has an exponential distribution with an average time to failure of 5 years, so that l51/55.2.a. What is the probability that this type of switch fails before year 4?b. What is the probability that this type of switch will fail after 6
24. 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
23. Tall or Short? Do Americans tend to vote for the taller of the two major candidates in a presidential election?In 53 of our presidential elections for which the heights of all the major-party candidates are known, 28 of the winners were taller than their opponents.2 Assume that Americans are
Using Table 1 in Appendix I, find the exact values for the binomial probabilities. Then approximate the probabilities using the normal approximation with the correction for continuity. Compare your answers. 14. P(x7) and P(x = 5) when n = 20 and p = .3
Using Table 1 in Appendix I, find the exact values for the binomial probabilities. Then approximate the probabilities using the normal approximation with the correction for continuity. Compare your answers. 15. P(x 10) when n = 20 and p=4
16. Earth Day A USA Today snapshot found that 47%of Americans associate “recycling” with Earth Day.9 Suppose a random sample of n550 adults are polled and that the 47% figure is correct. Use the normal curve to approximate the probabilities of the following events.a. Fewer than 30 individuals
17. Cell Phone Etiquette A Snapshot in USA Today indicates that 51% of Americans say the average person is not very considerate of others when talking on a cell phone.10 Suppose that 100 Americans are randomly selected. Find the approximate probability that 60 or more Americans would indicate that
18. 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 company. 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 A.
19. No Shows 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 person holding a reservation and
20. Genetic Defects Data indicate that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x560 children with the defect in a total of 50,000 examined.a. If the 50,000 children were a random sample from the population of children represented by past
21. 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 reservation. If the hotel accepts 215 reservations and there are only
22. 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 n5400 workers
2. Movie Start Times A movie has start times of 7:00, 7:15, and 7:30 p.m. You arrive randomly at the theater between 7:00 and 7:30 p.m. Let x be the time you arrive at the theater.a. What is the distribution of x?b. What is the probability that you wait less than 10 minutes until a movie starts?c.
3. Drill Bits An oil exploration 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 proportion of the company’s drill bits will fail before 60 hours of use?b. What
4. Restaurant Sales The daily sales total (excepting Saturday) at a small restaurant has a probability distribution that is approximately normal, with a mean m equal to $1230 per day and a standard deviation s equal to $120.a. What is the probability that the sales will exceed$1400 for a given
16. Loading Grain A grain loader can be set to discharge grain in amounts that are normally distributed, with mean m bushels and standard deviation equal to 25.7 bushels. If a company wishes to use the loader to fill containers that hold 2000 bushels of grain and wants to overfill only one
17. How Many Words? A publisher has discovered that the number of words contained in new manuscripts is approximately normally distributed, with a mean equal to 20,000 words in excess of that specified in the author’s contract and a standard deviation of 10,000 words. If the publisher wants to be
18. 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
19. The Freshman Class The admissions office of a small college is asked to accept deposits from a number of qualified prospective freshmen so that, with probability about .95, the size of the freshman class will be less than or equal to 1200. Suppose the applicants constitute a random sample from
20. Normal Distribution? The chest measurements for 5738 Scottish militiamen in the early 19th century are given here.16 Chest sizes are measured in inches, and each observation reports the number of soldiers with that chest size.Notice the approximate normality of the histogram of the 5738 chest
21. Normal Distribution? continued Assume that the chest measurements in Exercise 20 are normally distributed with a mean of m 539.83 and a standard deviation of s 52.05.a. What proportion of the observations would lie between 36.5 and 43.5 inches?b. Between what two measurements would 95% of the
1. If the average C grade is centered 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
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 summary statistics follows.For ease of calculation, round the number of standard deviations for C grades to 6.5
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
15. Elevator Capacities A study indicates that if eight people occupy an elevator, the probability distribution of the total weight of the eight people is approximately normally distributed with a mean equal to 545 kilograms and a standard deviation of 45 kilograms. What is the probability that the
14. Faculty Salaries In 2016, the National Center for Educational Statistics indicated that the average salary for Assistant Professors at public 4-year colleges was$83,398.15 Suppose that these salaries are normally distributed with a standard deviation of $4000.a. What proportion of assistant
5. Garage Door Openers Most users of automatic garage door openers activate their openers at distances that are normally distributed with a mean of 9 meters and a standard deviation of 3.3 meters. To minimize interference with other remote-controlled devices, the manufacturer is required to limit
6. Servicing Automobiles The length of time required to run an 8000-kilometer check and to service an automobile has a mean equal to 1.4 hours and a standard deviation of .7 hour. What is the probability that the next customer requiring an 8000-kilometer check and service will have to wait longer
7. TV Viewers An advertising agency has stated that 20% of all television viewers watch a given program.In a random sample of 1000 viewers, x5184 viewers were watching the program. Do these data present sufficient evidence to contradict the advertiser’s claim?
8. Snacking and TV 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 persons and matched them by weight and gender in
9. Tax Audits How does the IRS decide on the percentage of income tax returns to audit for each state? Suppose they do it by randomly selecting 50 values from a normal distribution with a mean equal to 1.55% and a standard deviation equal to .45%.a. What is the probability that a particular state

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