A restaurant is about to close, but it must wait until all 8 remaining customers have...

A restaurant is about to close, but it must wait until all 8 remaining customers have left. Starting now, each customer’s remaining time in the restaurant is exponentially distributed with mean fifteen minutes. If the customers leave independently of one another, find the probability that (a) after 2 hours the restaurant is still open; (b) after 1 hour, the restaurant is still waiting on exactly 2 customers.

Solutions

Expert Solution

a) Probability that after 2 hours that is 120 minutes, the restaurant is still open is computed here as:

= 1 - Probability that all 8 remaining customers leave within 2 hour period

Therefore 0.002681 is the required probability here.

b) Probability that after an hour that is 60 minutes, there are exactly 2 customers left is computed here as:

= Number of ways to choose 6 of the 8 customers * Probability that 6 out of the 8 customers finish in the first 60 minutes * Probability that 2 customers finish after 60 minutes

Therefore 0.008407 is the required probability here.

orchestra answered 2 years ago

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