Question

a given exam has a normal distribution with a mean of 70 and a standard deviation of 10. a sample of size 25 is selected. what percentage of the time would you expect the mean of this sample size to fall below 66?

Answer 1

we would expect the mean of the sample to fall below 66 about 5% of the time

Explanation:

To answer this question, we can use the 68-95-99.7 rule, which states that in a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

In this case, the mean of the sample is 70 and the standard deviation is 10, so the values that fall within one standard deviation of the mean are between 60 and 80. The values that fall below 66 are outside of this range, so we need to determine what percentage of the values fall within two standard deviations of the mean.

The values that fall within two standard deviations of the mean are between 50 and 90, so the percentage of values that fall below 66 is approximately (100 - 95) = 5%.

Therefore, we would expect the mean of the sample to fall below 66 about 5% of the time.