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 7.2 minutes and standard deviation 2.5 minutes. Suppose that a random sample of n = 49 customers is observed. Find the probability that the average waiting time in line for these customers is, (a) Less than 9 minutes (b) Between 4 and 9 minutes Water use in Phoenix in the summer is normally distributed with a mean of 300 million gallons per day and a standard deviation of 50 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons (a) What is the probability that a day requires more water than is stored in city reservoirs? (b) what amount of water use that is exceeded with 90% probability?

Explanation / Answer

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Normal dist params are given:

Mean = 300 million

Stdev = 50 million

Capacity = 350 million

a. P(X>350) = P(Z> 350-300 / 50) = P(Z>1) = .16

So, .16 is the probability that a day requires more water than is stored in city res.

b. Let c be the amount of water use such that it is exceeded by 90% probability

So, P(X>c) = .90

P(Z> (c-300)/50 ) = .90

So, Z = -1.28

(c-300)/50 = -1.28

c = 50*-1.28+300 = 236

So, amount of water use that is exceeded with 90% probability is 236

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