Question

At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 18 minutes and a standard deviation of 4minutes. Using the empirical rule, determine the interval of minutes that the middle68% of customers have to wait.Submit Answer

Answer 1

(14, 22)

Explanation:

The amount of time that customers have to wait for their food is normally distributed with:

• Mean = 18 minutes

,

• Standard deviation = 4 minutes.

The Empirical Rule

For normal distributions, the empirical rule states that:

• 68% of observed data points will lie inside one standard deviation of the mean.

,

• 95% will fall within two standard deviations

,

• 99.7% will occur within three standard deviations.

By the empirical rule, 68% of observed data points will lie inside one standard deviation of the mean.

Therefore, the interval of minutes that the middle 68% of customers have to wait is:

`(\mu-\sigma,\mu+\sigma)=(18-4,18+4)=(14,22)`

The interval is (14, 22).