# Estimating Population Mean and Distribution

1) A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled "3 pounds". Of course he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.

A) What is the estimated population mean.

B) Determine a 95 percent confidence interval for the population mean.

2. A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

3. A national manufacturer of unattached garages discovered that the distribution of the lengths of time it takes two construction workers to erect the Red Barn model is approximately normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the garages take between 30 and 34 hours to erect?

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#### Solution Preview

1.

A) Estimate of population mean = sample mean according to central limit theorem. Hence answer is 3.01

B) 95% confidence interval for mean

According to central limit theorem, the sample mean is normally distributed with mean = population mean and standard

deviation = sample sd/sqrt(n) = 0.03/sqrt(36) = 0.03/6 = 0.005

z ...

#### Solution Summary

The solution examines estimating the population mean and determining the normal distribution. The percent of invoices paid on time is determined.