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business statistics a first course

Questions and Answers of Business Statistics A First Course

Determine how large a simple random sample must be in order to estimate a population mean or proportion at specified levels of accuracy and confidence.
Decide whether the standard normal distribution or the t distribution should be used in constructing a given confidence interval.
Use the t distribution in constructing a confidence interval for a population mean.
Use the standard normal distribution in constructing a confidence interval for a population mean or proportion.
Explain the difference between a point estimate and an interval estimate for a population parameter.
Determine the effect on the sampling distribution when the samples are relatively large compared to the population from which they are drawn.
Explain the central limit theorem and its relevance to the shape of the sampling distribution of a mean or proportion.
Understand and determine the sampling distribution of proportions for samples from a given population.
Understand and determine the sampling distribution of means for samples from a given population.
Understand that the sample mean or the sample proportion can be considered a random variable.
6.4Construct contingency tables.
6.4Construct a dotplot and a scatter diagram.
6.4Visually represent data by using graphs and charts.
6.4• Construct a stem-and-leaf diagram to represent data.
6.4Construct relative and cumulative frequency distributions.
6.4Construct a frequency distribution and a histogram.
6.4 Repeat Applet Exercise 6.1 for k values of 6 through 12, in each case identifying the actual binomial probability that there will be no more than k females in the sample.For each value of k, also
6.3 With n 5 100 and 5 0.6, what is the actual binomial probability that there are no more than k 5 60 females in the sample of 100? How does this compare with the corresponding probability using
6.2 With n 5 5 and 5 0.6, what is the actual binomial probability that there are no more than k 5 3 females in the sample of 5? How does this compare with the corresponding probability using the
6.1 With n 5 15 and 5 0.6, as in the example in Section 7.4, what is the probability that there are no more than k 5 9 females in the sample of 15 walkers? How does this compare with the
5.4 Drag the left and right edges of the shaded area so that the left boundary corresponds to z 5 0 and the right boundary corresponds to z 5 11.0. What probability is now associated with the shaded
5.3 By dragging the left and right edges of the shaded area, determine the probability that a randomly selected plane will have flown between 130 and 160 hours during the year. What values of z
5.2 With the mean and standard deviation set at 120 and 30, respectively, drag the edges of the shaded area so that its left boundary is at 120 and its right boundary is at 180.What is the
5.1 Using the text boxes, ensure that the mean is 120 and the standard deviation is 30, as in the distribution of flying hours in Figure 7.5. (Don’t forget to hit the Enter or Return key while the
8. Comparing the BOUNCE scores when BALL 5 1 through 200 to those when BALL 5 201 through 240, does it appear that the process may have changed in some way toward the end of the work shift? In what
7. Examining the graph and the horizontal lines drawn in part (6), does it appear that about 90% of the balls have BOUNCE scores between the two horizontal lines you’ve drawn, as the normal
6. On the graph obtained in part (5), draw two horizontal lines—one at each of the BOUNCE scores determined in part (3).
5. Using the computer, generate a line graph in which BOUNCE is on the vertical axis and BALL is on the horizontal axis.
4. What is the probability that, for three consecutive balls, all three will happen to score below the lower of the two values determined in part (3)?Two hundred forty golf balls have been subjected
3. Given the distribution of bounce test scores described above, what score value should be exceeded only 5%of the time? For what score value should only 5% of the balls do more poorly?
2. Repeat part (1), but use the normal approximation to the binomial distribution. Do the respective probabilities appear to be very similar?
1. A driving range has just purchased 100 golf balls. Use the computer and the binomial distribution in determining the individual and cumulative probabilities for x 5 the number of balls that scored
4.3 Using the two sliders, position the red curve so that its mean is as small as possible and its shape is as narrow as possible. Compare the numerical values of the mean and standard deviation to
4.2 Using the bottom slider, change the standard deviation so that it is greater than 1. How does the shape of the red curve compare to that of the blue curve?
4.1 Position the top slider at the far left, then gradually move it to the far right. What effect does this have on the mean of the distribution?
7.83 In Exercise 7.82, the company would like to put in a greater weight “cushion” to help protect itself from consumer advocates. If the company wants to have just 2% of the packages contain
7.77 The mileage death rate for motorcycle riders has been estimated to be about 39 deaths per 100 million miles of motorcycle travel. A national motorcycling association has 1200 members who travel
7.73 Given the results of Exercise 7.72, evaluate the claim made by the public relations agency.
7.71 Of the 1.0 million persons of voting age in Maine, 72% voted in the 2008 presidential election. For a randomly selected group of 30 Maine residents who were of voting age at that time, what is
7.70 For itemized tax returns in the $60,000–$75,000 income group for the most recent year reported, the average charitable contribution was $1935. Assume a normal distribution and a standard
7.69 During fiscal 2008, the average daily volume for FedEx Corporation was 7,000,000 packages per day.Assuming a normal distribution and a standard deviation of 800,000 packages per day, on what
7.67 It has been reported that the average monthly cell phone bill is $50. Assuming a normal distribution and a standard deviation of $10, what is the probability that a randomly selected cell phone
7.65 In Exercise 7.64, the maker of soft drink A claims its product to be “superior” to soft drink B. Given the results obtained in Exercise 7.64, do they appear to have a solid basis for their
7.60 A computer statistical package has simulated 2000 random observations from a normal distribution with 5 80 and 5 20. Sketch the approximate box-andwhisker display for the resulting data.
7.59 A computer statistical package has simulated 1000 random observations from a normal distribution with 5 50 and 5 10. Sketch the approximate box-andwhisker display for the resulting data.
7.57 During 2008, U.S. general aviation pilots had 1.20 fatal crashes per 100,000 flying hours. Harriet Arnold is president of Arnold’s Flying Service, a company that operates a total of 50
7.54 A random variable is Poisson distributed with 5 0.50 arrivals per minute. For the corresponding exponential distribution, and x 5 minutes until the next arrival, identify the mean of x and
7.53 A random variable is Poisson distributed with l 5 0.02 occurrences per minute. For the corre sponding exponential distribution, and x 5 minutes until the next occurrence, identify the mean of x
7.52 A random variable is Poisson distributed with l 5 1.5 occurrences per hour. For the corresponding exponential distribution, and x 5 hours until the next occurrence, identify the mean of x and
7.49 What is the relationship between the Poisson distribution and the exponential distribution?
7.46 The Electronic Industries Association reports that about 50% of U.S. households have a camcorder. For a randomly selected sample of 800 U.S. households, use the normal approximation to the
7.45 Of all individual tax returns filed in the United States during the 2009 tax filing season, 15.8% were prepared by H&R Block. For a randomly selected sample of 900 tax returns filed during this
7.44 About 40% of new single-family homes completed in the United States during 2007 were heated with electricity.For a randomly selected sample of 20 new singlefamily homes completed during that
7.43 Approximately 80% of American families have some form of life insurance coverage. For a randomly selected sample of n 5 15 families, and the discrete random variable x 5 the number of families
In a certain binomial distribution, 5 0.30 and n 5 20. In using the normal approximation,a. What are the mean and standard deviation of the corresponding normal distribution?b. If x 5 the number of
7.37 The KleerCo company in Exercise 7.36 would like to design a more durable pump so that no more than 2% of original-equipment pumps are returned under free warranty, and the standard deviation
7.32 For the normal distribution described in Exercise 7.12, what tax preparation fee would have been exceeded by 90% of the tax preparation customers?
For the normal distribution described in Exercise 7.11, what first-mortgage amount would have been exceeded by only 5% of the mortgage customers?
For the normal distribution described in Exercise 7.15, what commuting time will be exceeded on only 10%of Jamal’s commuting days?
Using the standard normal table, find the following probabilities associated with z:a. P(21.96 # z # 1.27)b. P(0.29 # z # 1.00)c. P(22.87 # z # 21.22)
Using the standard normal table, find the following probabilities associated with z:a. P(20.36 # z # 0.00)b. P(z # 20.36)c. P(z $ 20.43)
A continuous random variable, x, is normally distributed with a mean of 200 grams and a standard deviation of 25 grams. Convert each of the following x values into its corresponding z-score:a. x 5
A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score:a. x 5 $1000b. x
7.15 On average, commuters in the Los Angeles, California, area require 30.0 minutes to get to work.Assume a normal distribution with a standard deviation of 5.0 minutes and a randomly selected Los
7.14 The average American family of four spends $5000 per year on food prepared at home. Assuming a normal distribution with a standard deviation of $1000 and a randomly selected American family of
7.12 In 2009, the average charge for tax preparation by H&R Block, Inc. was $187. Assuming a normal distribution and a standard deviation of 5 $20, what proportion of H&R Block’s tax preparation
7.10 The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was $1.55. If we assume a normal distribution and a standard deviation of 5
7.9 If x is normally distributed with 5 25.0 and 5 5.0, determine the following:a. P(x $ 25.0)b. P(20.0 # x # 30.0)c. P(x # 30)d. P(x 5 26.2)e. P(15.0 # x # 25.0)f. P(x $ 15)
7.8 If x is normally distributed with 5 20.0 and 5 4.0, determine the following:a. P(x $ 20.0)b. P(16.0 # x # 24.0)c. P(x # 12)d. P(x 5 22.0)e. P(12.0 # x # 28.0)f. P(x $ 16)
7.7 Sketch two different normal distributions along a single x axis so that both of the following conditions are satisfied: (a) a 5 b and (b) a . b.
7.6 In the normal distribution, the probability that x will exceed ( 1 2) is the same as the probability that x will be less than ( 2 2). What characteristic of the normal distribution does this
7.5 It has been stated that the normal distribution is really a “family” of distributions. Explain.
7.4 What is the probability that a continuous random variable will take on any specific value? Explain your answer.
7.3 Why is the total area beneath a probability density function equal to 1.0?
7.1 What is the difference between a continuous probability distribution and a discrete probability distribution?
6.79 Use the computer in determining probabilities associated with the normal and exponential distributions.
6.79 Understand the nature and the applications of the exponential distribution, including its relationship to the Poisson distribution of Chapter 6.
6.80 J.D. Power and Associates’ Initial Quality Study reports that the industry-average problem rate for vehicles is 108 problems per 100 vehicles. The highestrated brand was Lexus, with a rate of
6.79 Use the standard normal distribution and z-scores to determine probabilities associated with the normal distribution.
6.79 Understand the nature and the applications of the normal distribution.
6.79 A tire manufacturer has advertised that only 2%of its tires have surface blemishes. Further, the manufacturer argues that tires with such blemishes are perfectly safe, and with only the physical
6.78 It has been estimated that 5% of people who are hospitalized pick up infections while in the hospital, and that 2.2 million people a year get sick and 88,000 die because of these infections.
6.74 A gorilla once made headlines in 400 newspapers and appeared on three national television shows after correctly “selecting” the winner of 13 out of 20 football games. He had made his
6.72 According to the U.S. Centers for Disease Control and Prevention, Americans 85 years of age and older experience flu-associated respiratory and circulatory illness at an annual rate of
6.71 The Bureau of Labor Statistics says that baggage handlers, trash haulers, and coal miners are among the occupations having the highest risk of a debilitating injury or illness. For coal miners
6.69 In 2004, 50% of all U.S. families had a net worth less than $93,000. What is the probability that exactly three of a randomly selected sample of five families would have a net worth less than
6.68 A large plumbing contractor buys eight 200-foot rolls from the producer described in Exercise 6.67.Determine the probability that no more than three of the eight rolls will be flawless.
6.62 Unknown to a quality-control inspector, 20% of a very large shipment of electric switches are defective.The inspector has been told to reject the shipment if, in a sample of 15 switches, 2 or
6.59 Twenty percent of the population of Maryland describe themselves as binge drinkers. For a randomly selected group of 5 Maryland residents, use the appropriate statistical table to describe the
6.58 During the 2009 tax filing season, 15.8% of all individual U.S. tax returns were prepared by H&R Block. For a random selection of 3 tax returns, describe the probability distribution for x 5 the
6.57 In Exercise 6.56, suppose that three of the customers are interested in the same car, and that they will go elsewhere if it has already been sold. Would it be appropriate to use the binomial
6.55 During 2007, the crash rate for commuter air carriers was 1.0 per 100,000 flying hours. Assuming this rate continues, what is the probability that there will be no more than one crash in the
6.49 Taxicab drivers are more likely to be murdered on the job than members of any other occupation, even police officers and security guards. The annual murder rate for cab drivers is 30.0 homicides
6.48 The Federal Aviation Administration reports that American Airlines got 6.06 complaints of mishandled baggage per 1000 passengers in 2008. Assuming this rate applies to the next 500 passengers
6.47 According to the Mortgage Bankers Association of America, the foreclosure rate on home mortgages in 2007 was 2%. Assuming that this rate is applicable to a community where 500 homes have
6.44 During the 12 p.m.–1 p.m. noon hour, arrivals at a curbside banking machine have been found to be Poisson distributed with a mean of 1.3 persons per minute. If x 5 number of arrivals during a
6.43 The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x 5 the
6.42 Arrivals at a walk-in optometry department in a shopping mall have been found to be Poisson distributed with a mean of 2.5 potential customers arriving per hour. If x 5 number of arrivals during
6.41 In 2006, there were about 490 motor vehicle thefts for every 100,000 registrations. Assuming (1) a Poisson distribution, (2) a community with a comparable theft rate and 1000 registered motor
6.40 For a discrete random variable that is Poisson distributed with l 5 9.6, determine the following:a. P(x 5 7)b. P(x 5 9)c. P(x # 12)d. P(x $ 10)

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