Need help with D and E A sample of size ? = 81 is drawn from a population that has a mean ? = 43 and standard deviation ? = 3.1. The sample mean is 43.2. a. Find a 99% confidence interval for the mean...

Need help with D and E

A sample of size ? = 81 is drawn from a population that has a mean ? = 43 and standard
deviation ? = 3.1. The sample mean is 43.2.
a. Find a 99% confidence interval for the mean ? of the population.
______________________
b. What is the Error Bound of the Mean (EBM).
______________________
c. What sample size is required to limit the EBM to .50 or less?
______________________
d. When the confidence level increases, what happens to the width of the interval and
why?
e. How probable is it that we would get a sample mean of 44.00 or smaller given that
? = 43 and the sample size is 81?