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Statistics Principles And Methods 7th Edition Richard A. Johnson, Gouri K. Bhattacharyya - Solutions

An inspector samples bags of potato chips to see if they fall short of the weight, 14 ounces, printed on the bag. Samples of 20 bags are selected and the number with weight less than 14 ounces is recorded.(a) Make a p chart using the centerline and control limits calculated for p0 = .5.(b) Suppose
For each case, list the values of X and f(x) and examine if the specification represents a probability distribution. If it does not, state what properties are violated.(a) f(x) = 1/6(x - 1) for x = 1, 2, 3, 4(b) f{x) = 1/3(x - 3) for x = 2, 3, 4, 5(c) f(x) = 8/15 1/2x for x = 0, 1, 2, 3
Instead of performing a fixed number of Bernoulli trials, an experimenter performs trials until the first success occurs. The number of successes is now fixed at 1, but the number of trials Y is now random. It can assume any of the values 1, 2, 3, and so on with no upper limit.(a) Show that f(y) =
The probability distribution of X is given by the functionFind (a) P[X = 3] (b) P [X is even].
Refer to Exercise 5.7. Suppose that for each purchase P(B) = 1/2 and the decisions in different weeks are independent. Assign probabilities to the elementary outcomes and obtain the distribution of X.
Refer to Exercise 5.8. Assuming each choice is equally likely, determine the probability distribution of X.
Market researchers are concerned if people who view a commercial remember the product. They often make phone surveys two hours after a commercial is shown. Suppose that 20% of the people who watch one commercial remember the product two hours later. Four persons are randomly selected from those who
New video games are rated, by editors, at various Web sites (e.g., www.gamespot.com). You are equally interested in five games that received editors' ratings ofon a ten point scale. Suppose you decide to randomly choose two games to purchase at this time. Let X denote the sum of the ratings on the
Suppose, for a loaded die, the probabilities of the facesare in the ratios 3:1:1:1:1:3. Let X denote the number appearing on a single roll of the die.(a) Determine the probability distribution of X.(b) What is the probability of getting an even number?
Identify the variable as a discrete or a continuous random variable in parts (a)-(e). (a) The loss of weight following a diet program. (b) The magnitude of an earthquake as measured on the open-ended Richter scale. (c) The seating capacity of a roller coaster. (d) The number of cars sold at a
A surprise quiz contains three multiple-choice questions: Question 1 has four suggested answers, Question 2 has three, and Question 3 has two. A completely unprepared student decides to choose the answers at random. Let X denote the number of questions the student answers correctly.(a) List the
A probability distribution is partially given in the following table with the additional information that the even values of X are equally likely. Determine the missing entries in the table.
Consider the following setting of a random selection: A box contains 100 cards, of which 25 are numbered 1, 35 are numbered 2, 30 are numbered 3, 10 are numbered 4. One card will be drawn from the box and its number X observed. Give the probability distribution of X.
Two probability distributions are shown in the following tables. For each case, describe a specific setting of random selection (like the one given in Exercise 5.22) that yields the given probability distribution. and three do not. If three candidates are selected at random, find the probability
In a study of the life length of a species of mice, 120 newborn mice are observed. The numbers staying alive past the first, second, third, and fourth years are 106, 72, 25, and 0, respectively. Let X denote the life length (in discrete units of whole years) of this species of mice. Using these
Use the approximate probability distribution in Example 6 to calculate (a) P[X < 3] (b) P(X > 2] (c) P[2 < X < 3]
Of eight candidates seeking three positions at a counseling center, five have degrees in social science and there do not. If three candidates are selected at random, find the probability distributions of X, the number having social science degrees among the selected persons
Based on recent records, the manager of a car painting center has determined the following probability distribution for the number of customers per day. X f(x) 0........................................ .05 1........................................
Among cable TV customers, let X denote the number of television sets in a single-family residential dwelling. From an examination of the subscription records of 361 residences in a city, the frequency distribution is obtained.(a) Based on these data, obtain an approximate determination of the
Given the following probability distribution concerning the number of Web sites visited almost every day:(a) Construct the probability histogram.(b) Find E(X), Ïƒ2, and Ïƒ.
Two of the integers {1, 3, 5, 6, 7} are chosen at random without replacement. Let X denote the difference = largest - smallest.(a) List all choices and the corresponding values of X.(b) List the distinct values of X and determine their probabilities.
A wait person proposed a distribution for the number of meals served on a two-for-one deal.X f(x)2...........................34.......................... .56.......................... .18...........................1Find the mean and standard deviation.
In bidding for a remodeling project, a carpenter determines that he will have a net profit of $5000 if he gets the contract and a net loss of $86 if his bid fails. If the probability of his getting the contract is .2, calculate his expected return.
A book club announces a sweepstakes in order to attract new subscribers. The prizes and the corresponding chances are listed here (typically, the prizes are listed in bold print in an advertisement flyer while the chances are entered in fine print or not mentioned at all).Suppose you have just
Calculate the mean and standard deviation for the probability distribution of Example 5.
Referring to Exercise 5.27, find the mean and standard deviation of the number of customers.In Exercise 5.27 X f(x)0.........................................051........................................ .202........................................
A construction company submits bids for two projects. Listed here are the profit and the probability of winning each project. Assume that the outcomes of the two bids are independent.(a) List the possible outcomes (win/not win) for the two projects and find their probabilities. (b) Let X denote the
Refer to Exercise 5.35, but suppose that the projects are scheduled consecutively with A in the first year and B in the second year. The company's chance of winning project A is still .50. Instead of the assumption of independence, now assume that if the company wins project A, its chance of
Upon examination of the claims records of 280 policy holders over a period of five years, an insurance company makes an empirical determination of the probability distribution of X = number of claims in five years.x
Suppose the probability distribution of a random variable X is given by the functionF(x) = 12/25 ∙ 1/x for x = 1, 2, 3, 4 Calculate the mean and standard deviation of this distribution.
The probability distribution of a random variable X is given by the function(a) Calculate the numerical probabilities and list the distribution.(b) Calculate the mean and standard deviation of X.
The three finalists for an award are A, B, and C. They are rated by two judges. Each judge assigns the ratings 1 for best, 2 for intermediate, and 3 for worst. Let X denote the total score for finalist A (the sum of the ratings received from the two judges). (a) List all pairs of ratings that
Given here are the probability distributions of two random variables X and V.(a) From the X distribution, determine the distribution of the random variable 8 - 2X and verify that it coincides with the Y distribution. (Hence, identify Y = 8 - 2X.)(b) Calculate the mean and standard deviation of X
A communications systems salesperson contacts four businesses during a week. Each contact can result in either a sale, with probability .3, or no sale, with probability .7. Assume that the results for customer contacts are independent.(a) List the elementary outcomes and assign probabilities.(b) If
Refer to Exercise 5.41. Suppose the communications systems are priced at $5000, and let Y denote the salesman's total sales (in dollars) during a week.(a) Give the probability distribution of Y.(b) Calculate E(Y) and see that it is the same as 5000 × E(X).
Given the two probability distributions(a) Construct probability histograms. Which distribution has a larger spread? (b) Verify that both distributions have the same mean. (c) Compare the two standard deviations.
Is the model of Bernoulli trials plausible in each of the following situations? Discuss in what manner (if any) a serious violation of the assumptions can occur. (a) Seven friends go to a blockbuster movie and each is asked whether the movie was excellent. (b) A musical aptitude test is given to 10
In each case, examine whether or not repetitions of the stated experiment conform to the model of Bernoulli trials. Where the model is appropriate, determine the numerical value of p or indicate how it can be determined. (a) Roll a fair die and observe the number that shows up. (b) Roll a fair die
A jar contains 25 candies of which 6 are brown, 12 are yellow, and 7 are of other colors. Consider 4 successive draws of 1 candy at random from the jar and suppose the appearance of a yellow candy is the event of interest. For each of the following situations, state whether or not the model of
Refer to Exercise 5.47 and suppose instead that the mix consists of 2500 candies, of which 600 are brown, 1200 are yellow, and 700 are of other colors. Repeat parts (a)-(c) of Exercise 5.47 in this setting. In Exercise 5.47 A jar contains 25 candies of which 6 are brown, 12 are yellow, and 7 are of
From four agricultural plots, two are selected at random for a pesticide treatment. The other two plots serve as controls. For each plot, denote by S the event that it is treated with the pesticide. Consider the assignment of treatment or control to a single plot as a trial. (a) Is P(S) the same
Refer to Exercise 5.4. Suppose instead there are two finalists A and B and four judges. Each judge assigns the ratings 1 for the best and 2 for the worst finalists. (a) List all possible assignments of ratings to finalist A by the four judges. (b) List the distinct values of X, the total score of A.
Refer to Exercise 5.49. Now suppose for each plot a fair coin is tossed. If a head shows up, the plot is treated; otherwise, it is a control. With this manner of treatment allocation, answer parts (a) and (b). In Exercise 5.49 From four agricultural plots, two are selected at random for a pesticide
A market researcher intends to study the consumer preference between regular and decaffeinated coffee. Examine the plausibility of the model of Bernoulli trials in the following situations. (a) One hundred consumers are randomly selected and each is asked to report the types of coffee (regular or
A backpacking party carries three emergency signal flares, each of which lights with a probability of .98. Assuming that the flares operate independently, find: (a) The probability that at least one flare lights. (b) The probability that exactly two flares light.
Consider Bernoulli trials with success probability p = .3. (a) Find the probability that four trials result in all failures. (b) Given that the first four trials result in all failures, what is the conditional probability that the next four trials are all successes? (c) Find the probability that
According to numbers provided by the Bureau of Labor Statistics, the probability that three unrelated new businesses will last for five years is .216. What is the probability that all three have failed before that time? Assume that the conditions for Bernoulli trials hold.
A graphic designer makes a presentation to clients and this results in sales of her services in one-fourth of the cases. Assuming the results for different clients are independent (a) Find the probability that exactly 3 of the next 4 presentations result in sales. (b) Find the probability that none
An animal either dies (D) or survives (S) in the course of a surgical experiment. The experiment is to be performed first with two animals. If both survive, no further trials are to be made. If exactly one animal survives, one more animal is to undergo the experiment. Finally, if both animals die,
The accompanying table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy.Suppose that the selection of a person is considered a trial and the presence of the allergy is considered a success. For each case, identify the
For each situation, state whether or not a binomial distribution holds for the random variable X. Also, identify the numerical values of n and p when a binomial distribution holds. (a) A fair die is rolled 10 times, and X denotes the number of times 6 shows up. (b) A fair die is rolled until 6
Two brands of beverages, B and M, are popular with students. The owner of one campus establishment observes sales and, for each of three weekends, records which brand has the highest sales. List the possible outcomes, and for each outcome record the number of weekends X that the sales of B are
Construct a tree diagram for three Bernoulli trials. Attach probabilities in terms of p and q to each outcome and then table the binomial distribution for n = 3.
In each case, find the probability of x successes in n Bernoulli trials with success probability p for each trial. (a) X = 2 n = 3 P = .35 (b) X = 3 n = 6 P = .25 (c) X = 2 n = 6 P = .65
(a) plot the probability histograms for the binomial distributions for n = 5 and p equal to .2, .5, and .8.(b) Locate the means.(c) Find P[X > 4] for each of the three cases.
An interior designer makes a presentation to potential clients and this results in sales of her services in 35% of the cases. Let X denote the number of sales in the next four presentations. Assuming the results for different clients are independent, cal-culate the probabilities f(x) = P[X = x] for
About 75% of dog owners buy holiday presents for their dogs.2 Suppose n = 4 dog owners are randomly selected. Find the probability of: (a) Three or more buy their dog holiday presents. (b) At most three buy their dog holiday presents. (c) Find the expected number of persons, in the sample, who buy
According to a recent survey, outside of their own family members, 26% of adult Americans have no close friend to confide in. If this is the prevailing probability today, find the probability that in a random sample of n = 5 adults (a) Two or more have no close friend. (b) At most two have no close
Suppose 15% of the trees in a forest have severe leaf damage from air pollution. If 5 trees are selected at random, find the probability of: (a) Three of the selected trees have severe leaf damage. (b) No more than two have severe leaf damage.
Rh-positive blood appears in 85% of the white population in the United States. If 8 people are sampled at random from that population, find the probability that: (a) At least 6 of them have Rh-positive blood. (b) At most 3 of them have Rh-negative blood, that is, an absence of Rh positive.
Using the binomial table, find the probability of: (a) Four successes in 13 trials when p = .3. (b) Eight failures in 13 trials when p = .7. (c) Eight successes in 13 trials when p = .3. Explain why you get identical answers in parts (b) and (c).
Each week a grocery shopper buys either canned (C) or bottled (B) soft drinks. The type of soft drink purchased in 3 consecutive weeks is to be recorded. (a) List the sample space. (b) If a different type of soft drink is purchased than in the previous week, we say that there is a switch. Let X
According to' the U.S. Census Bureau, in 2011 about 10% of persons between 25 and 39 years old live alone. For a random sample of size n, use the binomial table to find the probability of (a) 1 or fewer persons living alone when n = 12. (b) 2 or more persons living alone when n = 12. (c) Find the
About 30% of adults say that reading is a favorite leisure activity. Let success be the outcome that reading is a favorite leisure activity. Find the probability that: (a) More than 5 trials are needed in order to obtain 3 successes. (In other words, the event is at most 2 successes in 5
A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probability that: (a) Fewer than 14 of them have had a physical examination in the past two years. (b) At least 17 of them have
Calculate the mean and standard deviation of the binomial distribution using the formulas in mean = np sd = √/np(1 - p) (a) Exercise 5.65 if n is changed to 20. (b) Exercise 5.70 when n = 20. (c) Exercise 5.71 when n = 40.
(a) For the binomial distribution with n = 3 and p = .6, list the probability distribution (x, f(x)) in a table.(b) From this table, calculate the mean and standard deviation by using the methods of Section 3.(c) Check your results with the formulas mean = np, sd = √npq.
Suppose that 20% of the college seniors support an increase in federal funding for care of the elderly. If 20 college seniors are randomly selected, what is the probability that at most 3 of them support the increased funding?
According to the Centers for Disease Control 50% of practicing physicians are in the specialty area of primary care. Assuming that the same rate prevails, find the mean and standard deviation of the number of physicians specializing in primary care out of a current random selection of 545 medical
According to the Mendelian theory of inheritance of genes, offspring of a dihybrid cross of peas could be any of the four types: round-yellow [RY], wrinkled-yellow (IVY), round-green (RG) and wrinkled-green (VKG), and their probabilities are in the ratio 9:3:3:1. (a) If X denotes the number of RY
The following table (see Exercise 5.58) shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. For each part below, find the mean and standard deviation of the specified random variable.(a) X stands for the number of persons
A child psychologist interested in how friends are selected studies groups of three children. For one group, Ann, Barb, and Carol, each is asked which of the other two she likes best. (a) Make a list of the outcomes. (Use A, B, and C to denote the three children.) (b) Let X be the number of times
Many computer packages produce binomial probabilities. We illustrate the MINITAB commands for obtaining the binomial probabilities with n = 5 and p = .33. The probabilities P[X = x] are obtained by first setting 0, 1, 2, 3, 4, 5 in CI and then selecting:which produces the output. Probability
Refer to the credit card application approval process on page 213 where unusual values are defined. (a) Show that if 4 is included as an unusual value, then the probability P[X < 4 or X > 13] is greater than .05. (b) Show that if 12 is included as an unusual value, then the probability P[ X < 3 or
Refer to the credit card application approval process on pages 213 and 214. (a) Make a p chart using the centerline and control limits calculated for p0 = .4. (b) Suppose the next five weeks bring 12, 10, 15, 11, and 16 applications requiring full review. Graph the corresponding proportions on your
Several fast food restaurants advertise quarter-pound hamburgers. This could be interpreted as meaning half the hamburgers made have an uncooked weight of at least a quarter-pound and half have a weight that is less. An inspector checks 20 uncooked hamburgers at each restaurant. (a) Make a p chart
Refer to Exercise 5.83. (a) What are the unusual values for the number of underweight hamburgers in the sample if they correspond to proportions outside of the control limits of the p chart? (b) Use the binomial table to find the probability of observing one of these unusual values.
A Poisson distribution with m = 5.5 governs the daily number of insurance claims handled by an adjuster. Determine the probability that she handles (a) 6 claims tomorrow. (b) 12 claims in the next two days. (c) 3 or fewer tomorrow.
The number of weekly breakdowns of a department's computing system is a random variable having a Poisson distribution with m = .4. What is the probability the computer will run for two consecutive weeks without a breakdown?
A Poisson distribution with m = 1.2 governs the number of fireflies that flash in a 10 second period during an August evening in the yard. Determine the probability that; (a) 2 fireflies flash. (b) Less than or equal 3 flash. (c) 6 fireflies flash in a 30 second period.
A Poisson distribution with m = 2.5 governs the yearly number of tornado touchdowns in a central area of the state. Find the probabilities P[X < 1] and P[X > 1].
For health reasons, homes need to be inspected for radon gas that decays and produces alpha particles. One device counts the number of alpha particles that hit its detector. To a good approximation, in one area, the count for the next week follows a Poisson distribution with mean 3. Determine (a)
Faced with a tight deadline on two major projects, you decide to hire two of the five available persons to help complete the work. They have 2, 3, 5, 3, and 2 years experience, respectively. Since their references are very similar, you decide to select two of these workers at random. Let X denote
Records over several years show that the probability is .00003 that a car will have a flat tire while driving through a long tunnel. About 16,000 cars use the tunnel each week. Determine the probability that 2 or more cars will have a flat next week (a) Using the Poisson approximation to the
According to a Federal Trade Commission Report, about. 13 % of the persons in the 20-29 year old age group filed identity theft complaints during 2011. From a random sample of n = 500 persons 20-29 years old, let X denote the number who filed an identity theft complaint last year. Assuming that the
Let X denote the difference (no. of heads - no. of tails) in three tosses of a coin. (a) List the possible values of X. (b) List the elementary outcomes associated with each value of X.
A large science department at the university made a list of its top 25 juniors and top 30 seniors. The first list contains 8 females and the second 10 females. One person is randomly selected from each list and the two selections are independent. Let X denote the number of females selected.(a) For
Refer to Exercise 5.93 but now suppose the sampling is done in two stages: First a list is selected at random and then, from that list, two persons are selected at random without replacement. Let Y denote the number of females in the sample.(a) List the elementary outcomes concerning the possible
A list of the world's 10 largest companies, in terms of value, contains 3 from the United States, 4 from China, and 1 each from Australia, Brazil, and the United Kingdom. A potential investor randomly selects 3 of the companies to research further.(a) Find the probability distribution of X, the
Refer to the monthly intersection accident data in Exercise 2.4. Considering an even longer record leads to a distribution for X = number of accidents in a month.Value xProbability f(x)0.............................081............................ .202............................
The following distribution has been proposed for the number of times a student will eat a gourmet restaurant dinner next week.x f(X)0..........................31..........................42..........................3(a) Calculate the mean and variance.(b) Plot the probability histogram and locate
Refer to Exercise 5.96. (a) List the x values that lie in the interval μ - σ to μ + σ and calculate P[u - σ < X < u + σ]. (b) List the x values that lie in the interval μ - 2σ to μ + 2σ and calculate P [μ - 2σ < X < μ + 2σ).
A student buys a lottery ticket for $1. For every 1000 tickets sold, two bicycles are to be given away in a drawing.(a) What is the probability that the student will win a bicycle?(b) If each bicycle is worth $200, determine the student's expected gain.
Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?
Males 20 to 29 years old have a mean height of 69.5 inches with a standard deviation of 3.1 inches. Females 20 to 29 years old have a mean height of 64.4 inches with a standard deviation of 3.0 inches. (Based on Statistical Abstract of the U.S. 2012, Table 209.) (a) Find the standardized variable
Find the area under the standard normal curve to the left of (a) z = 1.26 (b) z = .26 (c) z = -1.71 (d) z = -2.43
Find the area under the standard normal curve to the left of (a) z = .63 (b) z = 1.03 (c) z = -1.03 (d) z = -1.35
Find the area under the standard normal curve to the right of (a) z = 1.16 (b) z = .64 (c) z = -1.71 (d) z = -1.525 (interpolate)
Find the area under the standard normal curve to the right of (a) z = .63 (b) z = 2.63 (c) z = -1.23 (d) z = 1.635 (interpolate)
Find the area under the standard normal curve over the interval (a) z = -.75 to z = .75 (b) z = -1.09 to z = 1.09 (c) z = .32 to z = 2.65 (d) z = -.745 to z = 1.244 (interpolate)

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