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Business Statistics In Practice 6th Edition Bruce Bowerman, Richard O'Connell - Solutions

According to the Associated Press report (in Exercise 4.22), 47 percent of parents who have purchased TV sets after V-chips became standard equipment in January 2000 are aware that their sets have V-chips, and of those who are aware of the option, 36 percent have programmed their V-chips. Using
Fifteen percent of the employees in a company have managerial positions, and 25 percent of the employees in the company have MBA degrees. Also, 60 percent of the managers have MBA degrees. Using the probability formulas, a. Find the proportion of employees who are managers and have MBA degrees. b.
Consider Exercise 4.14 (page 170). Using the results in Table 4.4 (page 171), estimate the probability that a randomly selected 21- to 49-year-old consumer would a. Give the phrase a rating of 4 or 5 given that the consumer is male; give the phrase a rating of 4 or 5 given that the consumer is
In a survey of 100 insurance claims, 40 are fire claims (FIRE), 16 of which are fraudulent (FRAUD). Also, there are a total of 40 fraudulent claims.a. Construct a contingency table summarizing the claims data. Use the pairs of events FIRE and, FRAUD and.b. What proportion of the fire claims are
Recall from Exercise 4.3 that two randomly selected customers are each asked to take a blind taste test and then to state which of three diet colas (marked as A, B, or C) he or she prefers. Suppose that cola A's distributor claims that 80 percent of all people prefer cola A and that only 10 percent
A sprinkler system inside an office building has two types of activation devices, D1 and D2, which operate independently. When there is a fire, if either device operates correctly, the sprinkler system is turned on. In case of fire, the probability that D1 operates correctly is .95, and the
Two randomly selected grocery store patrons are each asked to take a blind taste test and to then state which of three diet colas (marked as A, B, or C) he or she prefers.a. Draw a tree diagram depicting the sample space outcomes for the test results.b. List the sample space outcomes that
Consider the share of core listenership by daypart information given in Figure 4.7 (page 177).a. Find an estimate of P(KPWR | 3-7 P.M.), the probability that a randomly selected Los Angeles resident who listens to the radio during the 3-7 P.M. daypart would name KPWR as his or her primary station
Figure 4.9 gives a portion of a title-by-title analysis for the song "We've Got It Goin' On" by the Backstreet Boys. The ratings information given in this figure is the same type given in Figure 4.8 (page 178) and explained in Example 4.16 (pages 176-179). Using the ratings information:a. Find an
In a murder trial in Los Angeles, the prosecution claims that the defendant was cut on the left middle finger at the murder scene, but the defendant claims the cut occurred in Chicago, the day after the murders had been committed. Because the defendant is a sports celebrity, many people noticed him
Suppose that A1, A2, A3, and B are events where A1, A2, and A3 are mutually exclusive andP (A1) = .2 P (A2) = .5 P (A3) = .3P (B|A1) = .02 P (B|A2) = .05 P (B = A3) = .04Use this information to find P (A1 | B), P(A2 | B) and P(A3 | B).
Suppose that a couple will have three children. Letting B denote a boy and G denote a girl:a. Draw a tree diagram depicting the sample space outcomes for this experiment.b. List the sample space outcomes that correspond to each of the following events:(1) All three children will have the same
Three data entry specialists enter requisitions into a computer. Specialist l processes 30 percent of the requisitions, specialist 2 processes 45 percent, and specialist 3 processes 25 percent. The proportions of incorrectly entered requisitions by data entry specialists 1. 2. and 3 are .03, .05,
Construct a tree diagram (like Figure 4.10) for the situation described in Exercise 4.46.
How many combinations of two high-risk stocks could you randomly select from eight high-risk stocks? If you did this, what is the probability that you would obtain the two highest-returning stocks?
Four people will enter an automobile showroom, and each will either purchase a car (P) or not purchase a car (N).a. Draw a tree diagram depicting the sample space of all possible purchase decisions that could potentially be made by the four people.b. List the sample space outcomes that correspond
Construct a tree diagram showing all possible combined movements for both stocks on a particular day (for instance, RR, RD, and so on, where the first letter denotes the movement of the first stock, and the second letter denotes the movement of the second stock).
If all outcomes are equally likely, find the probability that both stocks rise: that both stocks decline; that exactly one stock declines.
Find the probabilities you found in Exercise 4.53 by assuming that for each stock P(R) = .6, P(U) = .1, and P(D) = .3, and assuming that the two stocks move independently.
Assume that for the first stock (on a particular day)P(R) = .4, P(U) = -2, P(D) = .4and that for the second stock (on a particular day)P(R) = .8, P(U) = .1, P(D) = .1Assuming that these stocks move independently, find the probability that both stocks decline; the probability that exactly one stock
Using the information given in the AccuRatings report of Figure 4.3(given below), find estimates of each of the following:a. The probability that a randomly selected Los Angeles resident (12 years or older) would name station KLAX as the station that he or she listens to most.b. The probability
Repeat Exercises 4.56 through 4.59 for a randomly selected male aged 16 to 24. In general, do the tables on page 189 imply that labor force status and employment status depend upon educational attainment? Explain your answer.In exercise 4.56
Enterprise Industries has been running a television advertisement for Fresh liquid laundry detergent. When a survey was conducted, .21 of the individuals surveyed had purchased Fresh. .41 of the individuals surveyed had recalled seeing the advertisement, and .13 of the individuals surveyed had
A company employs 400 salespeople. Of these, 83 received a bonus last year. 100 attended a special sales training program at the beginning of last year, and 42 both attended the special sales training program and received a bonus. (Note: the bonus was based totally on sales performance.) a. What
Find estimates of P(5 | T), P(4 | T), P(3 | T), P(2 | T), and P(1 | T).
Let NT denote the event that a randomly selected listener is not tired of the song. Because we estimate that P(T) = .17 and P(T 11) = .70, we estimate that P(NT) = 1 - P(T) = .83 and P(NT | 1) = 1 - P(T | 1) = .30 a. Estimate P(NT | 5), P(NT | 4), P(NT | 3), and P(NT | 2). b. Estimate P(5 |NT), P(4
In this exercise we estimate the proportions of listeners familiar with the song who would give the song each rating. Using the definition of conditional probability, we estimate thatNote here that P(5 ( FAM) equals P(5) because the event 5 ( FAM and the event 5 are equivalent. That is, a randomly
Below we give two contingency tables of data from reports submitted by airlines to the U.S. Department of Transportation. The data concern the numbers of on-time and delayed flights for Alaska Airlines and America West Airlines at five major airports.a. What percentage of all Alaska Airlines
In the book Making Hard Decisions: An Introduction to Decision Analysis. Robert T. Clemen presents an example in which he discusses the 1982 John Hinckley trial. In describing the case, Clemen says:In 1982 John Hinckley was on trial, accused of having attempted to kill President Reagan. During
If A and B are events, define (in words) , A ∪ B, A ∩ B, and ∩ .
For each of the following, write out and graph the probability distribution of*. That is, list all the possible values of x and also list the corresponding probabilities. Then graph the distribution.a. Refer to Exercise 4.3 (page 163), and let x equal the number of patrons who prefer diet cola A.b.
For each of the following, find μx, σ2x, and σx Then interpret in words the meaning of μx and employ Chebyshev's rule to find intervals that contain at least 3/4 and 8/9 of the observed values of x.a. x = the number of patrons who prefer diet cola A as defined in Exercise 5.10a.b. x = the
Suppose hat probability distribution of a random variable x can be describe by the formula.P(x) = x/15for each of the values x = 1, 2, 3,4, and 5. For example, then, P(x = 2) = p(2) = 2/15.a. Write out the probability distribution of x.b. Show that the probability distribution of x satisfies the
The following table summarizes investment outcomes and corresponding probabilities for a particular oil well"X = the outcome in $p(x)-$40,000 (no oil)................ .2510,000 (some oil.................. .770,000 (much oil)................ .05a. Graph p(x); that is. graph the probability
In the book Foundations of Financial Management (7th ed.). Stanley B. Block and Geoffrey A. Hirt discuss risk measurement for investments. Block and Hirt present an investment with the possible outcomes and associated probabilities given in Table 5.4. The authors go on to say that the probabilities
An insurance company will insure a $50,000 diamond for its full value against theft at a premium of $400 per year. Suppose that the probability that the diamond will be stolen is .005. and let x denote the insurance company's profit.a. Set up the probability distribution of the random variable x.b.
In the book Foundations of Financial Management (7th ed.), Stanley B. Block and Geoffrey A. Hirt discuss a semiconductor firm that is considering two choices: (l) expanding the production of semiconductors for sale to end users or (2) entering the highly competitive home computer market. The cost
Five thousand raffle tickets are to be sold at $10 each to benefit a local community group. The prizes, the number of each prize to be given away, and the dollar value of winnings for each prize are as follows:If you buy one ticket, calculate your expected winnings. (Form the probability
Company A is considering the acquisition of two separate but large companies. Company B and Company C, having sales and assets equal to its own. Table 5.5 gives the probabilities of returns for each of the three companies under various economic conditions. The table also gives the probabilities of
Again consider Exercise 4.32 (page 181) and the title-by-title analysis of the song "We've Got It Goin' On" by the Backstreet Boys. Although not discussed in Exercise 4.32, Strategic Radio Research estimated the proportions of listeners familiar with the song who would give the song ratings of 5,
List the four characteristics of a binomial experiment.
Suppose that x is a binomial random variable with n = 5, p = .3, and q = .7.a. Write the binomial formula for this situation and list the possible values of x.b. For each value of x, calculate p(x), and graph the binomial distribution.c. Find P(x = 3).d. Find P(x < 3).e. Find P(x < 3).f. Find
Thirty percent of all customers who enter a store will make a purchase. Suppose that six customers enter the store and that these customers make independent purchase decisions.a. Let x = the number of the six customers who will make a purchase. Write the binomial formula for this situation.b. Use
The customer service department for a wholesale electronics outlet claims that 90 percent of all customer complaints are resolved to the satisfaction of the customer. In order to test this claim, a random sample of 15 customers who have filed complaints is selected.a. Let x = the number of sampled
The United States Golf Association requires that the weight of a golf ball must not exceed 1.62 oz. The association periodically checks golf balls sold in the United States by sampling specific brands stocked by pro shops. Suppose that a manufacturer claims that no more than 1 percent of its brand
An industry representative claims that 50 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners.a. Suppose that the representative's claim is true, and suppose
For each of the following, calculate μx, σ2x, and σx by using the formulas given in this section. Then (l) interpret the meaning of fig, and (2) find the probability that X falls in the interval [μx ± 2σx].a. The situation of Exercise 5.24, where x = the number of the six customers who will
The January 1986 mission of the Space Shuttle Challenger was the 25th such shuttle mission. It was unsuccessful due to an explosion caused by an O-ring seal failure.a. According to NASA, the probability of such a failure in a single mission was 1 /60.000. Using this value of p and assuming all
Classify each of the following random variables as discrete or continuous: a. x = the number of girls born to a couple who will have three children. b. x = the number of defects found on an automobile at final inspection. c. x = the weight (in ounces) of the sandwich meat placed on a submarine
Explain the assumptions that must be satisfied when a Poisson distribution adequately describes a random variable x. Discuss.
Suppose that x has a Poisson distribution with p. = 2.a. Write the Poisson formula and describe the possible values of x.b. Starting with the smallest possible value of x, calculate p(x) for each value of x until p(x) becomes smaller than .001.c. Graph the Poisson distribution using your results of
Suppose that x has a Poisson distribution with μ = 2.a. Use the formulas given in this section to compute the mean, μx, variance, σ2x, and standard deviation, σx.b. Calculate the intervals [μx ± 2σx] and [μx ± 3σx]. Then use the probabilities you calculated in Exercise 5.32 to find the
A bank manager wishes to provide prompt service for customers at the bank's drive-up window. The bank currently can serve up to 10 customers per 15-minute period without significant delay. The average arrival rate is 7 customers per 15-minute period. Let x denote the number of customers arriving
A telephone company's goal is to have no more than five monthly line failures on any 100 miles of line. The company currently experiences an average of two monthly line failures per 50 miles of line. Let x denote the number of monthly line failures per 100 miles of line. Assuming x has a Poisson
A local law enforcement agency claims that the number of times that a patrol car passes through a particular neighborhood follows a Poisson process with a mean of three times per nightly shift. Let x denote the number of times that a patrol car passes through the neighborhood during a nightly
When the number of trials, n, is large, binomial probability tables may not be available. Furthermore, if a computer is not available, hand calculations will be tedious. As an alternative, the Poisson distribution can be used to approximate the binomial distribution when n is large and p is small.
Suppose that an automobile parts wholesaler claims that .5 percent of the car batteries in a shipment are defective. A random sample of 200 batteries is taken, and four are found to be defective.a. Use the Poisson approximation discussed in Exercise 5.37 to find the probability that four or more
When can a hypergeometric distribution be approximated by a binomial distribution? Explain carefully what this means.
Suppose that x has a hypergeometric distribution with N = 8, r = 5. and n = 4. Find: a P (x = 0) b F (x = l) c F (x = 2) d P (x =3) e P (x = 4) f P (x ≥ 2) g P (x < 3) h P (x > 1)
Suppose that x has a hyper geometric distribution with N = 10, r = 4, and n = 3.a. Write out the probability distribution of .v.b. Find the mean μx variance σ2x, and standard deviation σx of this distribution.
An investor holds two stocks, each of which can rise (R), remain unchanged (U), or decline (D) on any particular day. Let x equal the number of stocks that rise on a particular day.a. Write the probability distribution of x assuming that all outcomes are equally likely.b. Write the probability
Repeat Exercise 5.46. letting x equal the number of stocks that decline on the particular day.In exercise 5.46a. Write the probability distribution of x assuming that all outcomes are equally likely.b. Write the probability distribution of .v assuming that for each stock P(R) = .6,P(U) = .1, and
Consider Exercise 5.46. and let x equal the number of stocks that rise on the particular day. Find μx, and σx, fora. The probability distribution of x in Exercise 5.46a.b. The probability distribution of x in Exercise 5.46b.c. The probability distribution of x in Exercise 5.46c.d. In which case
Suppose that the probability distribution of a random variable x can be described by the formulaP(x) = (x - 3)2 / 55for each of the values x = - 2, - 1, 0, 1. and 2.a. Write the probability distribution of x.b. Show that the probability distribution of x satisfies the properties of a discrete
A rock concert promoter has scheduled an outdoor concert on July 4th. If it does not rain, the promoter will make $30,000. If it does rain, the promoter will lose $15,000 in guarantees made to the band and other expenses. The probability of rain on the 4th is .4.a. What is the promoter's expected
The demand (in number of copies per day) for a city newspaper is listed below with corresponding probabilities:x = DemandP(x)50,000........................... .170,000.......................... .2590,000........................... .4110,000......................... .2130,000........................
United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 80 percent of all patients. Suppose that this drug is given to eight randomly selected patients who have been diagnosed with the viral infection.a. Let x equal the number of the
A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue.a. Suppose that the advocate's claim is true, and suppose that a
A retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The store's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is three per week. Let x denote the number of bad checks cashed per week. Assuming
Suppose that the number of accidents occurring in an industrial plant is described by a Poisson process with an average of 1.5 accidents every three months. During the last three months, four accidents occurred.a. Find the probability that no accidents will occur during the current three-month
A state has averaged one small business failure per week over the past several years. Let x denote the number of small business failures in the next eight weeks. Use the Poisson distribution to find P(x ≥ 17) if the mean number of small business failures remains what it has been. If .v actually
Describe how to compute the mean (or expected value) of a discrete random variable, and interpret what this quantity tells us about the observed values of the random variable. Discuss.
Explain whether each of the following is a valid probability distribution. If the probability distribution is valid, show why. Otherwise, show which conditions of a probability distribution are not satisfied.a.x p(x)-1.................. .20.................. .61..................
Consider each of the following probability distributions.a.x p(x)0.................. .21.................. .8b.xp(x)0.................. .251.................. .452.................... .23.................... .1c.XP(x)-2.................. .10................... .32..................
Suppose that an airline quotes a (light time of 2 hours. 10 minutes between two cities. Further-more, suppose that historical (light records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes. Letting the time unit be one
Refer to Exercise 6.11.a. Calculate the mean flight time and the standard deviation of the flight time.b. Find the probability that the flight time will be within one standard deviation of the mean.
A weather forecaster predicts that the May rainfall in a local area will be between three and six inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval three to six
Refer to Exercise 6.14.a. Calculate the expected May rainfall.b. What is the probability that the observed May rainfall will fall within two standard deviations of the mean? Within one standard deviation of the mean?
List five important properties of the normal probability curve.
In each case, sketch the two specified normal curves on the same set of axes: a. A normal curve with μ = 20 and σ = 3, and a normal curve with μ = 20 and σ = 6. b. A normal curve with μ = 20 and σ = 3, and a normal curve with μ = 30 and σ = 3. c. A normal curve with μ = 100 and σ = 10,
Let x be a normally distributed random variable having mean μ = 30 and standard deviation σ = 5. Find the z value for each of the following observed values of x:a. x = 25b. x = 15c. x = 30d. x = 40e. x = 50In each case, explain what the z value tells us about how the observed value of x compares
If the random variable z has a standard normal distribution, sketch and find each of the following probabilities:a. P (0 ≤ z ≤ 1.5)b. P (z ≥ 2)c. p (z ≤ 1.5)d. P (z ≥ -1)e. P (z ≤ -3)f. P (-1 ≤ z ≤ 1)g. P (-2.5 ≤ z ≤.5)h. P (1.5 ≤ z ≤ 2)i. P (-2 ≤ z ≤ -.5)
Suppose that the random variable c has a standard normal distribution. Sketch each of the following z points, and use the normal table to find each z point.a. z.01b. z.05c. z.02d. -z.01e. -z.05f. -z.10
Suppose that the random variable x is normally distributed with mean μ = 1,000 and standard deviation σ = 100. Sketch and find each of the following probabilities:a. P(1,000 ≤ x ≤ 1,200)b. P(x > 1,257)c. P(x < 1,035)d. P(857 ≤ x ≤ 1.183)e. P(x ≤ 700)f. P(812 ≤ x ≤ 913)g. p (x
Suppose that the random variable x is normally distributed with mean μ = 500 and standard deviation σ = 100. For each of the following, use the normal table to find the needed value k. In each case, draw a sketch.a. P(x ≥ k) = .025b. P(x ≥ k) = .05 c. P(x < k) = .025d. P(x ≤ k) = .015e.
Stanford-Binet IQ Test scores are normally distributed with a mean score of 1(H) and a standard deviation of 16.a. Sketch the distribution of Stanford-Binet IQ test scores.b. Write the equation that gives the z score corresponding to a Stanford-Binet IQ test score. Sketch the distribution of such z
Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes.a. What is the probability that weekly demand is(1) 959 boxes or less?(2) More than 1,004 boxes?(3) Less than 650 boxes or greater than 950 boxes?b.
The lifetimes of a particular brand of DVD player are normally distributed with a mean of eight years and a standard deviation of six months. Find each of the following probabilities where x denotes the lifetime in years. In each case, sketch the probability.a. P(l ≤ x ≤ 9)b. P(8.5 ≤ x ≤
United Motors claims that one of its cars, the Starbird 300, gets city driving mileages that are normally distributed with a mean of 30 mpg and a standard deviation of l mpg. Let x denote the city driving mileage of a randomly selected Starbird 300.a. Assuming that United Motors' claim is correct,
An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 percent. On the other hand, the firm reports that the yearly returns on tax-free municipal bonds are approximately
A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15.95 ounces and 16.05 ounces. Ajar is selected from the process every half hour until a sample of 100 jars is obtained. When the fills of the jars are measured, it is
A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 40,000 miles and a standard deviation of 4,000 miles. The company wishes to offer a guarantee
Recall from Exercise 6.32 that yearly returns on common stocks are normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent.a. What percentage of yearly returns are at or below the 10th percentile of the distribution of yearly returns? What percentage are at or
Consider the situation of Exercise 6.32. a. Use the investment broker's report to estimate the maximum yearly return that might be obtained by investing in tax-free municipal bonds. b. Find the probability that the yearly return obtained by investing in common stocks will be higher than the maximum
In the book Advanced Managerial Accounting, Robert P. Magee discusses monitoring cost variances. A cost variance is the difference between a budgeted cost and an actual cost. Magee describes the following situation:Michael Bitner has responsibility for control of two manufacturing processes. Every
Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation of $500. An insurance company has decided to oiler a health insurance premium reduction if a policyholder's health care expenses do not exceed a
Suppose that the 33rd percentile of a normal distribution is equal to 656 and that the 97.5th percentile of this normal distribution is 896. Find the mean μ and the standard deviation a of the normal distribution.We findP(x ≤ 63.5) = P (z ≤ - 3.85)Using the normal table, we find that the area
Explain how we make a continuity correction. Why is a continuity correction needed when we approximate a binomial distribution by a normal distribution? Discuss.
Suppose that x has a binomial distribution with n = 200 and p = .4.a. Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.b. Make continuity corrections for each of the following, and then use the normal approximation to the binomial to
Repeat Exercise 6.45 with n = 200 and p = .5.Repeat exercise 6.45Suppose that x has a binomial distribution with n = 200 and p = .4.a. Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.b. Make continuity corrections for each of the

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