Among U.S. cities with a population of more than 250,000 the mean one-way commut

ID: 3303569 • Letter: A

Question

Among U.S. cities with a population of more than 250,000 the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is in New York City, where the mean time is 38.5 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes.

What percent of the New York City commutes are for less than 26 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

What percent are between 26 and 34 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

What percent are between 26 and 45 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Explanation / Answer

a) we have, mean = = 38.5

S.D. = = 7.2

Sample mean = X = 26

P(x<26) = ?

So z = (X - ) / = (26 - 38.5) / 7.2 = -1.74

Putting the values in in normal distribution calculator or from the Z table we get

P(x<26) = 0.04093 = 4.09 %

(b) Solution: P(26<x<34) = P(x<34) – P(x<26)

z1 = (X1 - ) / = (26 - 38.5) / 7.2 = -1.74

z2 = (X2 - ) / = (34 - 38.5) / 7.2 = -0.625

Putting the values in in normal distribution calculator or from the Z table we get

P(26<x<34) = P(x<34) – P(x<26) = 22.51 %

Solution: P(26<x<45) = P(x<45) – P(x<26)

z1 = (X1 - ) / = (26 - 38.5) / 7.2 = -1.74

z2 = (X2 - ) / = (45 - 38.5) / 7.2 = 0.903

Putting the values in in normal distribution calculator or from the Z table we get

P(26<x<45) = P(x<45) – P(x<26) = 77.50 %

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Among U.S. cities with a population of more than 250,000 the mean one-way commut

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Among U.S. cities with a population of more than 250,000 the mean one-way commut

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