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

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?

32%
68%
95%
99.7%

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Aaliyah 7 days 2021-09-11T02:11:33+00:00 1 Answer 0

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    0
    2021-09-11T02:12:50+00:00

    Answer: Second Option

    68%

    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 <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

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