Answer:
a. Jean, because her commute is in the country.
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation , the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Whoever has the higher z-score will have the longer commute.
Mary:
Travels for 35 minutes. In big cities, average commutes are 40 minutes with a standard deviation of 15 minutes. This means that . So
Jean:
Travels for 30 minutes. In rural areas, the average commute is 25 minutes with a standard deviation of 6 minutes. This means that . So
Due to being in the Country, Jean's z-score is higher, so her commute is longer. The correct answer is given by option A.