Question

You have collected data about the fasting blood glucose (FBG) level of participants in your study. You are delighted to find that the variable is normally distributed. If the mean FBG is 82 and the standard deviation is 2.8 in what range would you expect to find the FBG of 68% of your study participants

Answer 1

Between 79.2 and 84.8.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 82, standard deviation of 2.8.

In what range would you expect to find the FBG of 68% of your study participants?

By the Empirical Rule, within 1 standard deviation of the mean, so:

82 - 2.8 = 79.2

82 + 2.8 = 84.8

Between 79.2 and 84.8.