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 24 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of customers have to wait between 19 minutes and 29 minutes?

at a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 24 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of customers have to wait between 19 minutes and 29 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 $x = 19$, $z_1=\frac{19 - 24}{5}=\frac{- 5}{5}=-1$. For $x = 29$, $z_2=\frac{29 - 24}{5}=\frac{5}{5}=1$.

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 68% of the data lies within 1 standard deviation of the mean. That is, $P(-1<Z<1)\approx68%$.

Answer:

68%