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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?

    d. Above how many seconds are 99% of the download times?

    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.

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    Solution Summary

    The solution provides step by step method for the calculation of confidence interval and normal probability. Formula for the calculation and Interpretations of the results are also included.