Question

Among the thirty largest U.S. cities, the mean one-way commute time to work is 25.8 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. Use Appendix B.3. What percent of the New York City commutes are for less than 26 minutes

Answer 1

4.093%

Explanation:

Here, we want to calculate the proportion of Newyork commutes that are less than 26 minutes

We start by calculating the z-score

z = (x - mean)/SD

here;

x = 26

mean = 38.5 minutes

SD = 7.2 minutes

Thus, we have;

z = (26-38.5)/7.2

z = -1.74

We proceed to use the standard normal distribution table to get the probability of P(x < -1.74)

That will be 0.04093

So the proportion will be this in %

That will be 4.093%