Statistics question -- ... If n=16, what is the probability that the sample mean is between 3% and 7%?...?

Question

The average year to date gain for bound mutual funds is 5.14%. Assume that the year to date returns are distributed as a normal random variable with a mean of 5.14 and a standard deviation of 4.00. If n=16, what is the probability that the sample mean is between 3% and 7%?

Answer 1

The new standard deviation, using the central limit theorem, is 4/sqrt(16)=1. Therefore,
(3-5.14)/1=-2.14 is the low z value
(7-5.14)/1=1.86
Therefore, using a z-table or the normalcdf function on the ti83, the answer is .9523