Refer to Exercise 7.69. Find the probability of the following events. a. The launch of the new product takes more than 105 days. b. The launch of the new product takes more than 92 days. c. The launch of the new product takes between 95 and 112 days. Data from Exercise 7.69: In preparing to launch a new product, a marketing manager has determined the critical path for her department. The activities and the mean and variance of the completion time for each activity along the critical path are shown in the accompanying table. Determine the mean and variance of the completion time of the project.
> The mean monthly income of graduates of professional and Ph.D. degrees is $6,000 according to a recent PEW Research Center survey. If these incomes are normally distributed with a standard deviation of $1,200, a. What proportion of incomes is greater tha
> Refer to Exercise 8.57. The manufacturer wants to provide guidelines to potential customers advising them of the minimum number of pages they can expect from each cartridge. How many pages should it advertise if the company wants to be correct 99% of the
> The number of pages printed before replacing the cartridge in a laser printer is normally distributed with a mean of 11,500 pages and a standard deviation of 800 pages. A new cartridge has just been installed. a. What is the probability that the printer
> The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable with a mean of 7.5 hours and a standard deviation of 2.1 hours. a. What proportion of A student’s stu
> Calculate the p-value of the test to determine that there is sufficient evidence to infer each research objective. Research objective: The population mean is greater than 7.5. σ = 1.5, n = 30, x = 8.5
> Refer to Exercise 8.54. Find the amount of sleep that is exceeded by only 25% of students. Data from Exercise 8.54: University and college students average 7.2 hours of sleep per night, with a standard deviation of 40 minutes. If the amount of sleep is
> University and college students average 7.2 hours of sleep per night, with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of university and college students sleep for more than 8 hours?
> Refer to Exercise 8.52. Find the probability of these events. a. A 2-year-old child is taller than 36 inches. b. A 2-year-old child is shorter than 34 inches. c. A 2-year-old child is between 30 and 33 inches tall. Data from Exercise 8.52: The heights o
> The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a ch
> The top-selling Red and Voss tire is rated 70,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 82,000 miles and a standard deviation of 6,400 miles. a. Wh
> Economists frequently make use of quintiles (i.e., the 20th, 40th, 60th, and 80th percentiles) particularly when discussing incomes. Suppose that in a large city household income are normally distributed with a mean of $50,000 and a standard deviation of
> Exercise 4.67 addressed the problem of setting an appropriate speed limit on highways. Automotive experts believe that the “correct” speed is the 85th percentile. Suppose that the speeds on a highway are normally distributed with a mean of 68 and a stand
> The Tesla Model S 85D is an electric car that the manufacturer claims can travel 270 miles on a single charge. However, the actual distance depends on a number of factors including speed and whether the car is driven in the city or on highways. Suppose t
> According to a PEW Research Center survey, the mean student loan at graduation is $25,000. Suppose that student loans are normally distributed with a standard deviation of $5,000. A graduate with a student loan is selected at random. Find the following p
> SAT scores are normally distributed with a mean of 1,000 and a standard deviation of 300. Find the quartiles.
> Calculate the p-value of the test to determine that there is sufficient evidence to infer each research objective. Research objective: The population mean is not equal to 1,500. σ = 220, n = 125, x = 1525
> Refer to Exercise 8.44. If we wanted to be sure that 98% of all bulbs last longer than the advertised figure, what figure should be advertised? Data from Exercise 8.44: The lifetimes of lightbulbs that are advertised to last for 5,000 hours are normally
> The lifetimes of lightbulbs that are advertised to last for 5,000 hours are normally distributed with a mean of 5,100 hours and a standard deviation of 200 hours. What is the probability that a bulb lasts longer than the advertised figure?
> Refer to Exercise 8.42. How long do the longest 10% of calls last? Data from Exercise 8.42: The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the
> The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the probability that a call a. lasts between 5 and 10 minutes. b. lasts more than 7 minutes. c. l
> Xis normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1, 100?
> Xis normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?
> Find z.28.
> Find z.065.
> Find z.03.
> Calculate the p-value of the test to determine that there is sufficient evidence to infer each research objective. Research objective: The population mean is less than 250. σ = 40, n = 70, x = 240
> calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 50 H1: μ < 50 σ = 15, n = 100, x = 48, α = .05
> Find the probabilities. P(Z < 1.65)
> Find the probability. P(Z < 1.61)
> The following is a graph of a density function. a. Determine the density function. b. Find the probability that X is greater than 10. c. Find the probability that X lies between 6 and 12. .10- 0- 20
> The following density function describes the random variable X. a. Graph the density function. b. Find the probability that X lies between 1 and 3. c. What is the probability that X lies between 4 and 8? d. Compute the probability that X is less than 7.
> The following function is the density function for the random variable X: a. Graph the density function. b. Find the probability that X lies between 2 and 4. c. What is the probability that X is less than 3? * - 1 fAx) = 1<x < 5 8 %3D 00
> Use a computer to find the following probabilities. a. P(F600, 800 > 1.1) b. P(F35, 100 > 1.3) c. P(F66, 148 > 2.1) d. P(F17, 37 > 2.8)
> Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 70 H1: μ > 70 σ = 20, n = 100, x = 80, α = .01
> Use a computer to find the following probabilities. a. P(F7, 20 > 2.5) b. P(F18, 63 > 1.4) c. P(F34, 62 > 1.8) d. P(F200, 400 > 1.1)
> Use a computer to find the following values of F. a. F.01, 100, 150 b. F.05, 25, 125 c. F.01, 11, 33 d. F.05, 300, 800
> A random variable has the following density function. f(x) = 1 − .5x 0 < x < 2 a. Graph the density function. b. Verify that f(x) is a density function. c. Find P(X > 1). d. Find P(X < .5). e. Find P(X = 1.5).
> Use the F table (Table 6) to find the following values of F. a. F.025, 8, 22 b. F.05, 20, 30 c. F.01, 9, 18 d. F..025, 24, 10
> Use the F table (Table 6) to find the following values of F. a. F.05, 3, 7 b. F.05, 7, 3 c. F.025, 5, 20 d. F.01, 12, 60
> Use a computer to find the following probabilities. Pržso > 250) b. Рзб > 25) Przoo > 500) d. Pi20 > 100) a. с.
> Use a computer to find the following probabilities. P > 80) b. Pz00 > 125) P(ss > 60) d. P(xio00 > 450) a. с.
> Use a computer to find the following values of χ2. a. χ2 .99, 55 b. χ2 .05, 800 c. χ2 .99, 43 d. χ2 .10, 233
> Use a computer to find the following values of χ2. a. χ2 .25, 66 b. χ2 .40, 100 c. χ2 .50, 17 d. χ2 .10, 17
> Use the χ2 table (Table 5) to find the following values of χ2. a. χ2 .90, 26 b. χ2 .01, 30 c. χ2 .10, 1 d. χ2 .99, 80 Data from Table 5: TABLE 8.5 Critical Values of x35, a and x35
> Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 100 H1: μ ≠ 100 σ = 10, n = 100, x = 100, α = .05
> Let X represent the result of the toss of a fair die. Find the following probabilities. a. P(X = 1) b. P(X = 6)
> Draw a diagram that shows the sampling distribution representing two unbiased estimators, one of which is relatively efficient.
> The random variable X is exponentially distributed with λ = 3. Sketch the graph of the distribution of X by plotting and connecting the points representing f(x) for x = 0, .5, 1, 1.5, and 2.
> Refer to Exercise 7.70. Find the quartiles of the time to complete the research project. Data from Exercise 7.70: A professor of business statistics is about to begin work on a new research project. Because his time is quite limited, he has developed a
> The mean and variance of the time to complete the project in Exercise 7.68 was 145 minutes and 31 minutes2. What is the probability that it will take less than 2.5 hours to overhaul the machine? Data from Exercise 7.68: The operations manager of a large
> Refer to Exercise 8.9. The operations manager labels any week that is in the bottom 20% of production a “bad week.” How many metric tons should be used to define a bad week? Data from Exercise 8.9: The weekly output of a steel mill is a uniformly distri
> In a survey of consumer finances, it was determined that the average household debt is $250,000. If household debt is normally distributed with a standard deviation of $30,000 determine the quintiles.
> The annual rate of return on a mutual fund is normally distributed with a mean of 14% and a standard deviation of 18%. a. What is the probability that the fund returns more than 25% next year? b. What is the probability that the fund loses money next yea
> Refer to Exercise 8.71. Any marble ryes that are unsold at the end of the day are marked down and sold for half-price. How many loaves should the bakery prepare so that the proportion of days that result in unsold loaves is no more than 60%? Data from E
> Every day a bakery prepares its famous marble rye. A statistically savvy customer determined that daily demand is normally distributed with a mean of 850 and a standard deviation of 90. How many loaves should the bakery make if it wants the probability o
> The average North American loses an average of 15 days per year to colds and flu. The natural remedy echinacea reputedly boosts the immune system. One manufacturer of echinacea pills claims that consumers of its product will reduce the number of days los
> Define relative efficiency.
> A professor of statistics noticed that the marks in his course are normally distributed. He has also noticed that his morning classes average 73%, with a standard deviation of 12% on their final exams. His afternoon classes average 77%, with a standard d
> A factory’s worker productivity is normally distributed. One worker produces an average of 75 units per day with a standard deviation of 20. Another worker produces at an average rate of 65 per day with a standard deviation of 21. What is the probability
> Repeat Exercise 9.64 assuming that the standard deviations are 12 and 16, respectively. Data from Exercise 9.64: Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from
> Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from each population, what is the probability that the mean of sample 1 is greater than the mean of sample 2? Populatio
> The operations manager of a plant making cellular telephones has proposed rearranging the production process to be more efficient. She wants to estimate the time to assemble the telephone using the new arrangement. She believes that the population standa
> The label on 1-gallon cans of paint states that the amount of paint in the can is sufficient to paint 400 square feet. However, this number is quite variable. In fact, the amount of coverage is known to be approximately normally distributed with a standa
> A medical researcher wants to investigate the amount of time it takes for patients’ headache to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She belie
> Draw diagrams representing what happens to the sampling distribution of a consistent estimator when the sample size increases.
> A statistics professor wants to compare today’s students with those 25 years ago. All his current students’ marks are stored on a computer so that he can easily determine the population mean. However, the marks 25 years ago reside only in his musty files
> The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviat
> A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses is about 10 pounds. How large a sample should he take
> Review Exercises 10.54 and 10.55. Describe what happens to the confidence interval estimate when a. the standard deviation is equal to the value used to determine the sample size. b. the standard deviation is smaller than the one used to determine the sa
> a. Repeat part (b) of Exercise 10.54 after discovering that the population standard deviation is actually 100. b. Repeat part (b) of Exercise 10.48 after discovering that the population standard deviation is actually 400.
> a. A statistics practitioner would like to estimate a population mean to within 10 units. The confidence level has been set at 95% and = 200. Determine the sample size. b. Suppose that the sample mean was calculated as 500. Estimate the population mean
> Review Exercises 10.51 and 10.52. Describe what happens to the confidence interval estimate when a. the standard deviation is equal to the value used to determine the sample size. b. the standard deviation is smaller than the one used to determine the sa
> a. Repeat part (b) in Exercise 10.51 after discovering that the population standard deviation is actually 5. b. Repeat part (b) in Exercise 10.45 after discovering that the population standard deviation is actually 20. Data from Exercise 10.51: a. Deter
> a. Determine the sample size necessary to estimate a population mean to within 1 with 90% confidence given that the population standard deviation is 10. b. Suppose that the sample mean was calculated as 150. Estimate the population mean with 90% confiden
> Review the results of Exercise 10.49. Describe what happens to the sample size when a. the population standard deviation decreases. b. the confidence level decreases. c. the bound on the error of estimation decreases.
> Define consistency.
> a. A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. What sample size should be used? b. Re-do part (a) changing the standard deviation to 50. c.
> Review Exercise 10.47. Describe what happens to the sample size when a. the population standard deviation increases. b. the confidence level increases. c. the bound on the error of estimation increases.
> a. Determine the sample size required to estimate a population mean to within 10 units given that the population standard deviation is 50. A confidence level of 90% is judged to be appropriate. b. Repeat part (a) changing the standard deviation to 100. c
> The sponsors of television shows targeted at the children’s market wanted to know the amount of time children spend watching television because the types and number of programs and commercials are greatly influenced by this information. As a result, it w
> Registered Retirement Savings Plan are retirement plans that defer taxes. Many Canadians rely on these plans for their retirement. To measure how these are doing, a random sample of 60-yearold Canadians was drawn and asked to report the total value of th
> How much do American families spend on entertainment each month. A survey was conducted and the amounts spent on entertainment in the previous month were recorded. Assuming that the population standard deviation is $50 determine the 99% confidence interv
> The rising cost of electricity is a concern for homeowners. An economist wanted to determine how much electricity has increased over the past 5 years. A survey was conducted with the percentage increase recorded. Assuming that the population standard dev
> A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assuming that incomes are normally distributed with a standard deviation of $30,000, determine the 90% confidence interval estimate of the mean annual
> One measure of physical fitness is the amount of time it takes for the pulse rate to return to normal after exercise. A random sample of 100 women age 40 to 50 exercised on stationary bicycles for 30 minutes. The amount of time it took for their pulse ra
> The image of the Japanese manager is that of a workaholic with little or no leisure time. In a survey, a random sample of 250 Japanese middle managers was asked how many hours per week they spent in leisure activities (e.g., sports, movies, television).
> Draw a sampling distribution of a biased estimator.
> A time study of a large production facility was undertaken to determine the mean time required to assemble a cell phone. A random sample of the times to assemble 50 cell phones was recorded. An analysis of the assembly times reveals that they are normall
> As part of a project to develop better lawn fertilizers, a research chemist wanted to determine the mean weekly growth rate of Kentucky bluegrass, a common type of grass. A sample of 250 blades of grass was measured, and the amount of growth in 1 week wa
> A statistics professor is in the process of investigating how many classes university students miss each semester. To help answer this question, she took a random sample of 100 university students and asked each to report how many classes he or she had m
> In an article about disinflation, various investments were examined. The investments included stocks, bonds, and real estate. Suppose that a random sample of 200 rates of return on real estate investments was computed and recorded. Assuming that the stan
> In a survey conducted to determine, among other things, the cost of vacations, 64 individuals were randomly sampled. Each person was asked to compute the cost of her or his most recent vacation. Assuming that the standard deviation is $400, estimate with
> A survey of 400 statistics professors was undertaken. Each professor was asked how much time was devoted to teaching graphical techniques. We believe that the times are normally distributed with a standard deviation of 30 minutes. Estimate the population
> Because of different sales ability, experience, and devotion, the incomes of real estate agents vary considerably. Suppose that in a large city the annual income is normally distributed with a standard deviation of $15,000. A random sample of 16 real est
> One of the few negative side effects of quitting smoking is weight gain. Suppose that the weight gain in the 12 months following a cessation in smoking is normally distributed with a standard deviation of 6 pounds. To estimate the mean weight gain, a ran
> Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in
> It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. The amount of time to complete a random sample of 10 oil changes was recorded and listed here. Compute the 99% confidenc
> Draw a sampling distribution of an unbiased estimator.
> The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 15 salespeople was taken, and the number of cars each sold is listed here. Find the 95% confidence interval estimate of t
> Among the most exciting aspects of a university professor’s life are the departmental meetings where such critical issues as the color of the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked
