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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?

32%
68%
95%
99.7%

User Mogul
by
8.8k points

1 Answer

5 votes

Answer: Second Option

68%

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 pizzas are delivered between 24 and 30 minutes

User Werner
by
8.2k points

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