1. For a sample of n = 6, list the six Z values.
   Use Excel to solve 6.17, 6.21, and 6.22
   6.17 A problem with a telephone line that prevents a customer form receiving or making calls is disconcerting to both the customer and the telephone company. The data at the top of page 198 (inserted below), represent two samples of 20 problems reported to two different offices of a telephone company. The time to clear these problems from the customers’ lines is recorded in minutes. PHONE
   Central Office I Time to Clear Problems (minutes)
   1.48 1.75 0.78 2.85 0.52 1.60 4.15 3.97 1.48 3.10
   1.02 0.53 0.93 1.60 0.80 1.05 6.32 3.93 5.45 0.97
   Central Office II time to Clear Problems (minutes)
   7.55 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02
   
   3.75 0.65 1.92 0.60 1.53 4.23 0.08 1.48 1.65 0.72
   For each of the two central office locations, decide whether the data appear to be approximately normally distributed by:
   1. evaluating the actual versus theoretical properties.
   2. constructing a normal probability plot.

6.22 The following data represent the electricity cost in dollars during the month of July 2004 for a random sample of 50 two-bedroom apartments in a large city: UTILITY

96 171 202 178 147 102 153 197 127 82

157 185 90 116 171 111 148 213 130 165

141 149 206 175 123 128 144 168 109 167

95 163 150 154 130 143 187 166 139 149

108 119 183 151 114 135 191 137 129 158

Decide whether the data appear to be approximately normally distributed by:

1. evaluating the actual versus theoretical properties.
2. constructing a normal probability plot.

*6.33 The Wall Street Journal reported that almost all the major stock market indexes had posted strong gains in the last 12 months. The one-year return for the S&P 500, a group of 500 very large companies, was approximately + 27%. The one-year return in the Russell 2000, a group of 2000 small companies, was approximately + 52%. Historically, the one-year returns are approximately normal. The standard deviation in the S&P 500 returns is approximately 20%, and in the Russell 2000 the standard deviation is approximately 35%.

1. What is the probability that a stock in the S&P 500 gained 30% or more in the last year? Gained 60% or more in the last year?
2. What is the probability that a stock in the S&P 500 lost money in the last year? Lost 30% or more?
3. Repeat (a) and (b) for a stock in the Russell 2000.
4. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation.

7.11 In a random sample of 64 people, 48 are classified as "successful." If the population proportion is 0.70,

1. determine the sample proportion p of "successful" people.

b. determine the standard error of the proportion.

7.19 According to the National Restaurant Association, 20% of fine-dining restaurants have instituted policies restricting the use of cell phones. If you select a random sample of 100 fine-dining restaurants,

1. what is the probability that the sample has between 15% and 25% that have established policies restricting cell phone use?
2. the probability is 90% that the sample percentage will be contained within what symmetrical limits of the population percentage?
3. the probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage?

7.53 DiGiorno’s frozen pizza has some of the most creative and likeable advertisements on television. USA Today’s Ad Track claims that 20% of viewers like the ads "a lot." Suppose that a sample of 400 television viewers is shown the advertisements. What is the probability that the sample will have between

1. 18% and 22% who like the ads "a lot"?

b. 16% and 24% who like the ads "a lot"?

c. 14% and 26% who like the ads "a lot"?

d. 12% and 28% who like the ads "a lot"?

8.19 The following data represent the monthly service fee in dollars if a customer’s account falls below the minimum required $1,500 balance for a sample of 26 banks for direct-deposit customers. BANKCOST2

12 8 5 5 6 6 10 10 9 7 10

7 7 5 0 10 6 9 12 0 5 10

8 5 5 9

1. Construct a 95% confidence interval for the population mean monthly service fee in dollars if a customer’s account falls below the minimum required balance.
2. Interpret the interval constructed in (a).

8.21 In New York state, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage where the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of 1 month, a random sample of 27 approved policies was selected INSURANCE and the total processing time in days recorded:

73 19 16 64 28 28 31 90 60 56 31

56 22 18 45 48 17 17 17 91 92 63

50 51 69 16 17

1. Construct a 95% confidence interval estimate of the mean processing time.
2. What assumption must you make about the population distribution in (a)?
3. Do you think that the assumption made in (b) is seriously violated? Explain.

8.59 Starwood Hotels conducted a survey of 401 top executives who play golf. Among the results were the following:

329 cheat at golf

329 hate others who cheat at golf

289 believe business and golf behavior parallel

80 would let a client win to get business

40 would call in sick to play golf

Construct 95% confidence interval estimates for each of these questions. What conclusions can you reach about CEO’s attitudes toward golf from these results?

* 8.69 A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. In this example, the label weight on the package indicates that the mean amount is 5.5 grams of tea in a bag. If the bags are underfilled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. On the other hand, if the mean amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 170 bags a minute). The following table provides the weight in grams of a sample of 50 tea bags produced in one hour by a single machine. TEABAGS

Weight of Tea Bags in Grams

5.65 5.44 5.42 5.40 5.53 5.34 5.54 5.45 5.52 5.41

5.57 5.40 5.53 5.54 5.55 5.62 5.56 5.46 5.44 5.51

5.47 5.40 5.47 5.61 5.53 5.32 5.67 5.29 5.49 5.55

5.77 5.57 5.42 5.58 5.58 5.50 5.32 5.50 5.53 5.58

5.61 5.45 5.44 5.25 5.56 5.63 5.50 5.57 5.67 5.36

1. Construct a 99% confidence interval estimate of the population mean weight of the tea bags.
2. Is the company meeting the requirement set forth on the label that the mean amount of tea in a bag is 5.5 grams?

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