45. 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?

b. Based on your answer to part (a), is there convincing evidence that less than 90% of all orders from this company are shipped within three working days? Explain your reasoning.