Suppose you wish to estimate a population mean correct to

Suppose you wish to estimate a population mean correct to within .15 with a confidence level of .90. You do not know σ2, but you know that the observations will range in value between 31 and 39.
a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to be conservative to ensure that the sample size will be ample for achieving the desired accuracy of the estimate. [Hint: Using your knowledge of data variation from Section 2.5, assume that the range of the observations will equal 4σ.]
b. Calculate the approximate sample size, making the less conservative assumption that the range of the observations is equal to 6σ.