An investment analyst would like to estimate the average amountinvested in a particular mutual fund by institutional investors. Arandom sample of 15 institutional investors' portfolios has beenchosen. The observed sample mean of the amounts invested in themutual fund by these 15 investors is $11.32 million and theobserved sample standard deviation is $4.4 million. Assume the portfolios are distributed normally. Required:
a. Construct a 90% confidence interval for the mean amount invested by all institutional investors in the mutual fund.
b. Determine the required sample size in order to estimate the mean amount invested by all institutional investors in this mutual fund to within $500,000, at the 95% confidence level.