Conditional Probability 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 518 minutes with s 5 4 minutes. You assume that the x distribution is approximately normal.

Hint: Recall the conditional probability rule from Section 4.2, P A B P A B P B

( | ) 5

( and )

( )

.

So for example,

. . 5

. .

.

5

.

.

( 17 | 10)

( 17 and 10)

( 10)

( 17)

( 10)

.

P x x P x x P x P x P x

(a) What is the probability that the waiting time will exceed 20 minutes, given that it has exceeded 15 minutes? Hint: Compute P(x . 20 | x . 15).

(b) What is the probability that the waiting time will exceed 25 minutes, given that it has exceeded 18 minutes? Hint: Compute P(x . 25 | x . 18).

AppendixLO1