Please show the work please

Suppose you wish to estimate a population mean correct to within 0.16 with a confidence level of .90. You do not know sigma squared 2, but you know that the observations will range in value between34 and 42. Complete parts a and b.

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: assume that the range of the observations will equal 4

b. Calculate the approximate sample size, making the less conservative assumption that the range of the observations is equal to 6