Question

In a recent survey of 655 working Americans ages 25-34, the average weekly amount spent on lunch was 43.76 with standard deviation 2.67. The weekly amounts are approximately bell-shaped. (c) Between what two values will approximately 95% of the amounts be?

Answer 1

Between 38.42 and 49.1.

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 43.76, standard deviation of 2.67.

Between what two values will approximately 95% of the amounts be?

By the Empirical Rule, within 2 standard deviations of the mean. So

43.76 - 2*2.67 = 38.42

43.76 + 2*2.67 = 49.1

Between 38.42 and 49.1.