Question

at a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 26 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of customers have to wait between 16 minutes and 36 minutes?

Explanation:

Step1: Calculate number of standard - deviations from the mean

First, find how many standard - deviations 16 minutes and 36 minutes are from the mean. The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value.
For $x = 16$, $z_1=\frac{16 - 26}{5}=\frac{- 10}{5}=-2$.
For $x = 36$, $z_2=\frac{36 - 26}{5}=\frac{10}{5}=2$.

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 95% of the data lies within 2 standard - deviations of the mean, that is, in the interval $(\mu - 2\sigma,\mu + 2\sigma)$. Since $z_1=-2$ and $z_2 = 2$, the interval (16, 36) is within 2 standard - deviations of the mean.

Answer:

95%