SOLUTION: 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

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Question 1092102: 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 38.8 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.7 minutes.

a.
What percent of the New York City commutes are for less than 27 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Percent %

b.
What percent are between 27 and 35 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Percent %

c.
What percent are between 27 and 43 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Percent %

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd, used for the whole problem.
z< (27-38.8)/7.7=-11.8/7.7=-1.53
That probability is 0.0630 or 6.30%
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between 27 and 35 requires z for 35 which is (35-38.8)/7.7 or -3.8/7.7=-0.49
z between -1.53 and -0.49 is 0.2491 or 24.91%
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between 27 and 43 requires z for 43 which is (43-38.8)/7.7=4.2/7.7=0.55
the z between -1.53 and 0.55 is 0.6458 or 64.58%