The average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes, with a standard deviation of 3.6 minutes. Assume wait time is normally distributed. When a patron arrives at the restaurant for dinner, find the probability that the patron will have to wait less than 18 minutes or more than 25 minutes.

Question

Mathematics

Dominique Kirby

17 April, 08:08

The average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes, with a standard deviation of 3.6 minutes. Assume wait time is normally distributed. When a patron arrives at the restaurant for dinner, find the probability that the patron will have to wait less than 18 minutes or more than 25 minutes.

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Answers (1)

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Sabine · Answer 1

0.40

Step-by-step explanation:

Find the z-scores.

z = (x - μ) / σ

z₁ = (18 - 23.5) / 3.6

z₁ = - 1.53

z₂ = (25 - 23.5) / 3.6

z₂ = 0.42

Use a table or calculator to find the probability.

P (Z 0.42) = 0.0630 + (1 - 0.6628) = 0.4002

The probability is approximately 0.40.