Draw a picture of the distribution for each problem with mean and standard deviations labeled and relevant areas shaded. Show exactly what you entered in to the calculator to arrive at your result, including what function you used and what numbers you entered. Round all decimals to 3 places. Read the questions carefully!

A union wants to get an idea of how many hours per month the average employee is absent from work. 325 employees are randomly selected, and the number of hours each employee misses work is recorded. If the sample has a mean of 8.1 hours and a standard deviation of 5.8 hours,

1. Give a 95% confidence interval for the mean number of hours per month an employee is absent.

2. Give a 99% confidence interval for the mean number of hours per month an employee is absent. How does this interval differ from the one above? Why does this happen?

3. Suppose we know that the population standard deviation for the number of missed hours per month is actually 5.4. Give a 95% confidence interval for the mean number of hours per month an employee is absent, given this new piece of information.