1) The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical r

Question

1) The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?
2)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?

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Eliza 2 weeks 2021-09-11T02:32:51+00:00 1 Answer 0

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    2021-09-11T02:34:01+00:00

    Answer:

    1) 68%

    2) 68%

    Step-by-step explanation:

    1) The ages of trees

    We know the mean and the standard deviation.

    The mean is:

    \mu=25

    The standard deviation is:

    \sigma=5

    The Z-score formula is:

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

    For x=20 the Z-score is:

    Z_{20}=\frac{20-25}{5}=-1

    For x=30 the Z-score is:

    Z_{30}=\frac{30-25}{5}=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 trees are between 20 and 30 years old

    2) Pizza delivery

    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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27:3+15-4x7+3-1=? ( )