Suppose you want to eat lunch at a popular restaurant. The restaurant does not take reservations, so there is usually a waiting time before you can be seated. Let x represent the length of time waiting to be seated. From past experience, you know that the mean waiting time is m = 18 minutes with s = 4 minutes. You assume that the x distribution is approximately normal.

(a) What is the probability that the waiting time will exceed 20 minutes, given that it has exceeded 15 minutes?

(b) What is the probability that the waiting time will exceed 25 minutes, given that it has exceeded 18 minutes?

(c) Review item 6, conditional probability, in the summary of basic probability rules at the end of Section 4.2. Note that

And show that in part (a),

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KA and H) KAM- P((x > 20) and (x > 15)) P(x > 15) P(x > 20) P(x > 15) Pa >20a >15) -