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

Click here to see ALL problems on Probability-and-statistics

Question 1091848: 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 38.7 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.3 minutes.

a.
What percent of the New York City commutes are for less than 29 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Percent %

b.
What percent are between 29 and 36 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Percent %

c.
What percent are between 29 and 44 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!
a. z=(x-mean)/sigma or (29-38.7)/7.3 or -9.7/7.3=-1.33; probability is z < -1.33 or 9.18%
b. z for 36 minutes is (36-38.7)/7.3 or -2.7/7.3 or -0.37. Want z in between -1.33 and -0.37. This is 26.39%
c.z for 44 minutes is (44-38.7)/7.3=5.3/73 or +0.73. Want z between -1.33 and +0.73. This is 67.55%