at a local restaurant, the amount of time that customers have to wait for their food is normally distributed…

at a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 46 minutes and a standard deviation of 3 minutes. using the empirical rule, what percentage of customers have to wait between 40 minutes and 52 minutes?

at a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 46 minutes and a standard deviation of 3 minutes. using the empirical rule, what percentage of customers have to wait between 40 minutes and 52 minutes?

Answer

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value. For $x = 40$, $z_1=\frac{40 - 46}{3}=\frac{-6}{3}=- 2$. For $x = 52$, $z_2=\frac{52 - 46}{3}=\frac{6}{3}=2$.

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 95% of the data lies within $z=-2$ and $z = 2$.

Answer:

95%