On-time shipping A mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit. The audit reveals that 86 of these orders were shipped on time.

(a) If the company really ships 90% of its orders on time, what is the probability that the proportion in an SRS of 100 orders is 0.86 or less? Show your work.

(b) A critic says, “Aha! You claim 90%, but in your sample the on-time percentage is lower than that. So the 90% claim is wrong.” Explain in simple language why your probability calculation in

(a) shows that the result of the sample does not refute the 90% claim.