Question

The mean commute time to work for residents of New York City is 34.3 minutes with a standard deviation of 8.86 minutes. The mean commute time to work for residents of San Diego is 23.5 minutes with a standard deviation of 6.41 minutes. A randomly selected New Yorker took 25.4 minutes while a randomly selected San Diegan took 17.7 minutes to commute to work. How much shorter was the San Diegan's commute time? Express the answer as decimal value rounded to the nearest tenth. Question 15 4 pts Revisit the previous problem. Assume each distribution in that problem is approximately normal. Relative to the city, who had the shorter commute? Do not just state the answer. Type up a mathematical justification for your answer. If you prefer to write the mathematical justification and upload it along with your work instead, feel free to do so.

Answer 1

The San Diegan's commute time was 7.7 minutes shorter than the New Yorker's commute time. Relative to their respective cities, the San Diegan had the shorter commute.

Step-by-step explanation:

To determine how much shorter the San Diegan's commute time was compared to the New Yorker's commute time, we subtract the San Diegan's commute time from the New Yorker's commute time:

25.4 - 17.7 = 7.7 minutes

Therefore, the San Diegan's commute time was 7.7 minutes shorter than the New Yorker's commute time.

In order to determine who had the shorter commute relative to the city, we compare each person's commute time to the mean commute time for their respective city.

For the New Yorker:

(25.4 - 34.3) / 8.86 = -1.01 (z-score)

For the San Diegan:

(17.7 - 23.5) / 6.41 = -0.91 (z-score)

Since both z-scores are negative, this indicates that both the New Yorker and the San Diegan have commute times below the mean for their respective cities.

However, the San Diegan's z-score (-0.91) is closer to 0 than the New Yorker's z-score (-1.01), indicating that the San Diegan's commute time is relatively closer to the mean commute time for San Diego compared to the New Yorker's commute time to the mean commute time for New York City.

Therefore, relative to their respective cities, the San Diegan had the shorter commute.