Students in an Introductory Statistics Class Were Asked to Report $99 \%$

Students in an introductory statistics class were asked to report the age of their mothers when they were born. Summary statistics include
Sample size: 28 students Sample mean: 29.643 years
Sample standard deviation: 4.564 years
a. Calculate the standard error of this sample mean.
b. Determine and interpret a 90\% confidence interval for the mother's mean age (at student's birth) in the population of all students at this university.
c. How would a $99 \%$ confidence interval compare to the $90 \%$ interval in terms of its midpoint and halfwidth?
d. Would you expect $90 \%$ of the ages in the sample to be within the $90 \%$ confidence interval? Explain why or why not.
e. Even if the distribution of mothers' ages were somewhat skewed, would this confidence interval procedure still be valid with these data? Explain why or why not.