Suppose that 40% of all U.S. employees contribute to a retirement plan (p = 0.40). (a) In a random sample of 100 employees, what is the approximate probability that at least half of those in the...

Suppose that 40% of all U.S. employees contribute to a retirement plan

(p = 0.40).
(a) In a random sample of 100 employees, what is the approximate probability that at least half of those in the sample contribute to a retirement plan? (Round your answer to four decimal places.)

(b)
Suppose you were told that at least 66 of the 100 employees in a sample from your state contribute to a retirement plan. Would you think

p = 0.40 for your state? Explain. (Round your answer to four decimal places.)
If  p = 0.40, the probability that at least 66 of the 100 employees in a sample from the state contribute to a retirement plan is

. Thus, it seems unlikely that  p = 0.40 for the state.