An analysis performed by Hewitt Associates indicated the median amount saved in a 401(k) plan by people 50 to 59 years old was $53,440. The average saved is $115,260 for that age group. Assume the standard deviation is $75,000.
a. Examining these statements, would it be possible to use a normal distribution to determine the proportion of workers who have saved more than $115,260? Support your assertions.
b. If it is possible to determine the probability that a sample of size 5 has an average amount saved in a 401(k) plan that is more than $115,260, do so. If not, explain why you are unable to do so.
c. Repeat the instructions in part b with a sample size of 35.