Lista de Exercícios de Normal

6.9 According to the Internal Revenue Service, income tax returns one year averaged $1,332 in refunds for taxpayers. One explanation of this figure is that taxpayers would rather have the government keep back too much money during the year than to owe it money at the end of the year. Suppose the average amount of tax at the end of a year is a refund of $1,332, with a standard deviation of $725. Assume that amounts owed or due on tax returns are normally distribute-

• What proportion of tax returns show a refund greater than $2,000?
• What proportion of the tax returns show that the taxpayer owes money to the government?
• What proportion of the tax returns show a refund between $100 and $700?

6.10 Toolworkers are subject to work-related injuries. One disorder, caused by strains to the hands and wrists, is called carpal tunnel syndrom- It strikes as many as 23,000 workers per year. The U.S. Labor Department estimates that the average cost of this disorder to employers and insurers is approximately $30,000 per injured worker. Suppose these costs are normally distributed, with a standard deviation of $9,000.

• What proportion of the costs are between $15,000 and $45,000?
• What proportion of the costs are greater than $50,000?
• What proportion of the costs are between $5,000 and $20,000?
• Suppose the standard deviation is unknown, but 90.82% of the costs are more than $7,000. What would be the value of the standard deviation?
• Suppose the mean value is unknown, but the standard deviation is still $9,000. How much would the average cost be if 79.95% of the costs were less than $33,000?

6.11 Suppose you are working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. Determine the value of x from the following information.

• 60% of the values are greater than x.
• x is less than 17% of the values.
• 22% of the values are less than x.
• x is greater than 55% of the values.

6.12 Suppose the annual employer 401(k) cost per participant is normally distributed with a standard deviation of $625, but the mean is unknown.

• If 73.89% of such costs are greater than $1,700, what is the mean annual employer 401(k) cost per participant?
• Suppose the mean annual employer 401(k) cost per participant is $2,258 and the standard deviation is $625. If such costs are normally distributed, 31.56% of the costs are greater than what value?

6.13 Suppose the standard deviation for Problem 6.7 is unknown but the mean is still 22 feet. If 72.4% of all U.S. Class A warehouses have a clear height greater than 18.5 feet, what is the standard deviation? 6.14 Suppose the mean clear height of all U.S. Class A warehouses is unkn

6.22 According to the Yankee Group, 53% of all cable households rate cable companies as good or excellent in quality transmission. Sixty percent of all cable households rate cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacte-

• What is the probability that more than 175 cable households rate cable companies as good or excellent in quality transmission?
• What is the probability that between 165 and 170 (inclusive) cable households rate cable companies as good or excellent in quality transmission?
• What is the probability that between 155 and 170 (inclusive) cable households rate cable companies as good or excellent in having professional personnel?
• What is the probability that fewer than 200 cable households rate cable companies as good or excellent in having professional personnel?

6.23 Market researcher Gartner Dataquest reports that Dell Computer controls 27% of the PC market in the United States. Suppose a business researcher randomly selects 130 recent purchasers of P-

• What is the probability that more than 39 PC purchasers bought a Dell computer?
• What is the probability that between 28 and 38 PC purchasers (inclusive) bought a Dell computer?
• What is the probability that fewer than 23 PC purchasers bought a Dell computer?
• What is the probability that exactly 33 PC purchasers bought a Dell computer?

6.24 A study about strategies for competing in the global marketplace states that 52% of the respondents agreed that companies need to make direct investments in foreign countries. It also states that about 70% of those responding agree that it is attractive to have a joint venture to increase global competitiveness. Suppose CEOs of 95 manufacturing companies are randomly contacted about global strategies.

• What is the probability that between 44 and 52 (inclusive) CEOs agree that compa- nies should make direct investments in foreign countries?
• What is the probability that more than 56 CEOs agree with that assertion?
• What is the probability that fewer than 60 CEOs agree that it is attractive to have a joint venture to increase global competitiveness?
• What is the probability that between 55 and 62 (inclusive) CEOs agree with that assertion?