Question

The times for the mile run of a large group of male college students are approximately Normal with mean 7.11 minutes and standard deviation 0.74 minutes.

Use the 68–95–99.7 rule to answer the following questions.
(Start by making a sketch like Figure 3.8.)

1. What range of times covers almost all (99.7%) of this distribution?
A. 5.63 to 8.59
B. 4.89 to 9.33
C. 6.37 to 7.85
D. 2.22 to 12

Answer 1

The rule is that for normally distributed data:

- 68% are in the range mean +/- 1*standard deviation
- 95% are in the range mean +/- 2*standard deviation
- 99.7% are in the range mean +/- 3*standard deviation

Then in this case the range is from 7.11 minutes - 3*0.74 minutes to 7.11 minutes + 3*0.74 minutes

This is, 7.11 - 2.22 to 7.11 + 2.22

Equal to 4.89 to 9.33

Then, the answer is the option B.