Question

(CO 1) In a normally distributed data set of how long customers stay in your store, the mean is 31.7 minutes and the standard deviation is 1.9 minutes. Within what range would you expect 95% of your customers to stay in your store

Answer 1

The range is between 27.9 minutes and 35.5 minutes.

Explanation:

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

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

95% of the measures are within 2 standard deviation of the mean.

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

In this problem, we have that:

Mean = 31.7 minutes

Standard deviation = 1.9 minutes.

Within what range would you expect 95% of your customers to stay in your store

Within 2 standard deviations of the mean.

Lower bound: 31.7 - 2*1.9 = 27.9 minutes

Upper bound: 31.7 + 2*1.9 = 35.5 minutes

The range is between 27.9 minutes and 35.5 minutes.