Question

Use the empirical rule to solve the problem. ed's monthly phone bill is normally distributed with a mean of $65 and a standard deviation of $11. what percentage of his phone bills are more than $76?

Answer 1

16% of his phone bills are more than $76

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 = 65

Standard deviation = 11

What percentage of his phone bills are more than $76?

76 = 65 + 11

So 76 is one standard deviation above the mean.

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than 1 standard deviation from the mean. Since the normal probability distribution is symmetric, 16% of them are more than 1 standard deviation below the mean and 16% are more than 1 standard deviation above the mean. So

16% of his phone bills are more than $76

Answer 2

By the empirical rule, 84% of the distribution is below one standard deviation above the mean.

16% of Ed's monthly phone bills are more than $76.