# Normal Probability, Confidence Interval & Sample Size

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1.(use the Normal Probability file)

In a recent year, about two-thirds of 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 normal random variable with a mean of $45.16 and a standard deviation of $10.00.

a)Find the probability that a household spent less than $25.00?

b)Find the probability that a household spent more than $50.00?

c)What portion of the households spent between $30.00 and $40.00?

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

2.(use the Normal Probability file)

The mean download time for the 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)99% of the download times are above how many seconds?

3.(use the confidence interval file)

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.995 gallon.

a)construct a 99% confidence interval estimate of the population mean amount of paint included in a 1-gallon can

b)on the basis of these results, do you think the manager has a right to complain to the manufacturer? Why?

4.(use the confidence interval file)

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 policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below and stored in the file insurance.xls:

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 of the mean processing time.

b) what assumption must you make about the population distribution in (a)?

5.(use the confidence interval file)

A large number of companies are trying to reduce the cost of prescription drug benefits by requiring employees to purchase drugs through a mandatory mail-order program. In a survey of 600 employees, 126 indicated that they either had a mandatory mail-order program in place or were adopting one by the end of 2004.

a)construct a 95% confidence interval for the population portion of employers who had a mandatory mail-order program in place or were adopting one by the end of 2004

6.(Use the sample sizes file)If the inspection division of a county 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?

7.(Use the sample sizes file)The U.S. Department of transportation defines an airline flight as being "on-time" if it lands less than 15 minutes after the scheduled time shown in the carrier's computerized reservation system. Cancelled and diverted flights are counted as late. A study of the 10 largest U.S. domestic airlines found Southwest Airlines to have the lowest proportion of late arrivals, at 0.1577. Suppose you were asked to perform a follow-up study for Southwest Airlines in order to update the estimated proportion of late arrivals. What sample size would you use in order to estimate the population proportion to within an error of

a)±0.06 with 95% confidence?

8.Use the "Cumba" data file to answer the following:

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

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

c)In one or two sentences, interpret the results.

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##### Solution Summary

The solution provides step by step method for the calculation of confidence interval, sample size and probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

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