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# Case Analysis Using Normal Distributions And T-Distributions

1. In order to efficiently bid on a contract, a contractor wants to be 99% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the population standard deviation o- is 4.5 hours. Find the minimum sample size "n" that is needed to estimate the average time.

2. An educational researcher is interested in estimating the population mean p, grade point average of high school students. He randomly selects 10 high school students, and records their grade point averages. The sample mean x = 2.54 with sample standard deviation s = 1.1098. Assume that grade point averages are normally distributed. Construct a 90% confidence interval for the population mean grade point average of all high school students. Decide whether the normal distribution or the t-distribution should be used.

#### Solution Summary

This solution calculates the minimum sample size needed to calculate an average time, and whether normal or t-distributions should be used to calculate the confidence level.

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