8.85 How often do women feel sad? A recent GSS asked,

“How many days in the past seven days have you felt sad?” The 816 women who responded had a median of 1, mean of 1.81, and standard deviation of 1.98. The 633 men who responded had a median of 1, mean of 1.42, and standard deviation of 1.83.

a. Find a 95% confidence interval for the population mean for women. Interpret.

b. Do you think that this variable has a normal distribution? Does this cause a problem with the confidence interval method in part a? Explain.