among us cities with a population Among U.S. cities with a population of more th

Question

among us cities with a population Among U.S. cities with a population of more than 250,000, the mean one-way commute time to work is 24.3 minutes. Two longest one-way travel time is New York City, where the mean time is 38.2 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7 0 minutes (a) What percent of the New York City commutes are for less than 28 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) Percent __________ % (b) What percent are between 28 and 33 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) Percent __________ % (c) What percent are between 28 and 46 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) Percent __________ %

Explanation / Answer

Solution:-

Given, Mean = 38.2

Standard deviation = 7

Using online normal distribution calculator,

(a) Cumulitive probability (X < 28) = 0.0725 or 7.25%

(b) Cumulitive probability (28 < X < 33) = 0.1562 or 15.62%

(c) Cumulitive probability (28 < X < 46) = 0.7949 or 79.49%

For the actual calculations for normal distribution, we calculate the value of z,

where z = (x – ) / , and for the corresponding z value we find out the p value, which is our cumulitive probability.

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