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Your mail-order company advertises that it ships 90% of its orders within three working days. You...

Your 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. Note: It could be assumed that it satisfies all four conditions of the Binomial experiment.

a) If the company really ships 90% of its orders on time, what is the probability that 86 or fewer in an SRS of

100 orders are shipped on time? (Hint: Consider Normal approximation) [4]

b) A critic says, “Aha! You claim 90%, but in your sample the on-time percent is only 86%. 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. [1]

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