A large firm has 10,000 employees. Although it provides health insurance, employees still spend personal income on medical expenses. Last year the

mean amount per employee spent on medical expenses was $52.5 with a standard deviation $12.0.

(a) What is the probability that a simple random sample of 36 employees will yield a mean between $50 and $55?

(b) What is the probability that a simple random sample of 36 employees will yield a mean greater than $60?

(c) What might be a problem if you use the normal distribution to make these calculations for a single person chosen at random from the

employee list?