The amount of time that a customer spends waiting at an airport check-in counter

Question

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. Suppose that a random sample of 49 customers is observed.

a.) What is the sampling distribution of the average waiting time of 49 customers?

b.) Find the probability that the average waiting time is less than 10 minutes.

c.) Find the probability that the average waiting time is between 5 and 10 minutes.

d.) Find the probability that the average waiting time is less than 6 minutes.

Explanation / Answer

a) It is a normal distribution with mean = 8.2

b) P(X < 10) = P(Z < (10-8.2)/1.5) = P(Z < 1.2) = 0.8849

c) P(5 < X < 10) = 0.8849 - P(X < 5) = 0.8849 - P(Z < (5-8.2)/1.5) = 0.8849 - P(Z < -2.13) = 0.8849 - 0.0165 = 0.8684

d) P(X < 6) = P(Z < -1.4667) = 0.0712

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