Question

Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?

Answer 1

Answer:

68% of the pizzas are delivered between 24 and 30 minutes

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

$\mu=27$

The standard deviation is:

$\sigma=3$

The Z-score formula is:

$Z = \frac{x-\mu}{\sigma}$

For $x=24$ the Z-score is:

$Z_{24}=\frac{24-27}{3}=-1$

For $x=30$ the Z-score is:

$Z_{30}=\frac{30-27}{3}=1$

Then we look for the percentage of the data that is between $-1$ deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of the pizzas are delivered between 24 and 30 minutes