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

Question

Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The 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.

What percent of the New York City commutes are for less than 28 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

What percent are between 28 and 33 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

What percent are between 28 and 46 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The 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.

Explanation / Answer

The probability that the commute is less than 30 minutes is the standard normal value N_Z for (30 - 38.3)/7.5

(30 - 38.3)/7.5 = -1.107

The standard normal tables give 0.1349 (I interpolated between the values of -1.10 and -1.11, which are .1357 and .1335, respectively). So it's about 13.5% of commutes.

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