Answer:
There is a 16.62% probability that it will take between 72 and 77 minutes to complete the test.
Explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by

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.
The length of time needed to complete a certain test is normally distributed with mean 74 minutes and standard deviation 12 minutes, so
.
Find the probability that it will take between 72 and 77 minutes to complete the test.
We have to subtract the pvalue of Z when X = 77 by the pvalue of Z when X = 72.
So
X = 77



has a pvalue of 0.5987.
X = 72



has a pvalue of 0.4325.
So, there is a 0.5987 - 0.4325 = 0.1662 = 16.62% probability that it will take between 72 and 77 minutes to complete the test.