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Confidence Interval & Normal Probability

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Q-3a. A stationery store wants to estimate the mean retail value of greeting cards purchased by its customers when they visit the store. A random sample of 15 customers indicates a mean amount of $2.55 with a standard deviation of $0.44 per customer per visit. Assuming a normal distribution, construct a 95% confidence interval estimate of the mean retail value of greeting cards purchased by its customers.

Q-3b. A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches, and the standard deviation of the length is 0.02 inches. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 11 inches or whether something has gone wrong in the production process to change the length of the paper produced. You select a random sample of 100 sheets, and the mean paper length is 10.998 inches. Construct a 95% confidence interval estimate for the population mean paper length.

Q-3c. A survey of 705 workers asked how much they used the Internet at work. 423 said they used it within limits, and 183 said that they did not use the Internet at work. Construct a 95% confidence interval estimate for the proportion of all workers who use the Internet within limits.

Q-3d. You are the designer for your company's web site. You have data to indicate that the mean download time for the homepage is 7 seconds and that the standard deviation of download time is 2.0 seconds. If we assume that the download times are normally distributed, what percent of users will wait between 5 and 10 seconds for the homepage to download?

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Solution Summary

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