# Statistics Problem Set: Developing Confidence Intervals

1. A car rental office checks out an average of 30 cars per day with a standard deviation of 8 cars. If a sample of 25 days of operation is selected and the sample mean is computed. What is the value for the standard error of the mean? What is the probability that the sample mean for the 25 days will be within 27 and 32 cars?

2. In an effort to estimate the mean annual amount spent per customer for groceries at a particular supermarket, data were collected for a sample of 100 households. The sample showed an average amount of $8,000. If the population standard deviation is $500. Develop an 80% then a 85% confidence interval estimate of the population mean annual amount spent. If the data were collected for a sample of 50 households rather than 100, develop an 85% confidence interval estimate of the population mean annual amount spent, assuming the population has a normal probability distribution

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1. A car rental office checks out an average of 30 cars per day with a standard deviation of 8 cars. If a sample of 25 days of operation is selected and the sample mean is computed,

(a) What is the value for the standard error of the mean?

Solution. Given that x-bar = 30, sigma = 8 and n = 25. Using a formula for the standard error of the mean: sigma_x-bar = sigma/(sqrt(n)) = 8/(sqrt(25)) = 1.6.

(b) What is the probability that the sample mean for the 25 days will be within 27 and 32 cars?

Solution. Let Z = (x-bar - 30)/1.6 . Then Z~N(0, 1). ...

#### Solution Summary

The expert develops confidence intervals and problem sets.