Question

If amount of utility bill is normally distributed with a mean of $105 and a standard deviation of $20. What percentage of your bills would you expect to be between $85 and $125?

Answer 1

68% of your bills between $85 and $125

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 = $105

Standard deviation = $20

What percentage of your bills would you expect to be between $85 and $125?

85 = 105 - 20

125 = 105 + 20

Within one standard deviation of the mean, so by the Empirical Rule, 68% of your bills between $85 and $125