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Normal Probability & Confidence Interval

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1.) In a recent year, about two-thirds of the U.S. households purchased ground coffee. Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a random normal variable with a mean of \$65.16 and a standard deviation of \$10.00.

a. Find the probability that the household spent less than \$35.00.

b. Find the probability that a household spent more than \$60.00.

d. 99% of the households spent less than what amount?

2.) The same article mentioned in problem 6.52 also reported that the mean download time for H&R Block Web site, www.hrblock.com, is 2.5 seconds. Suppose that the download time is normally distributed, with a standard deviation of 0.5 second. What is the probability that a download time is

a. less than 1 second?

b. between 0.5 and 1.5 seconds?

c. above 0.5 second?

4.) 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 in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policy to customers in a timely manner is critical to the profitability of this service to the bank. During a period of a month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below and stored in insurance:

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

a. Construct a 95% confidence interval estimate for the population mean processing time.

5.) If the inspection division of a country weights and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottles to within ±0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed.

6.) Use the 'Cumba' data file to answer the following:

-Using the age data only, conduct a 95% confidence interval of the mean age of employees at Cumba, Inc.

-Using the gender data only, conduct a 95% confidence interval of the proportion of female employees at Cumba, Inc.