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

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

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 = (x-\mu)/(\sigma)`

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

`Z_(24)=(24-27)/(3)=-1`

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

`Z_(30)=(30-27)/(3)=1`

Then we look for the percentage of the data that is between
`-1 <Z <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