The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical ru

Question

The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?

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Gianna 2 weeks 2021-09-11T02:44:16+00:00 1 Answer 0

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    2021-09-11T02:45:28+00:00

    Answer:

    95% of students are between 14 and 18 years old

    Step-by-step explanation:

    First we calculate the Z-scores

    We know the mean and the standard deviation.

    The mean is:

    \mu=16

    The standard deviation is:

    \sigma=1

    The z-score formula is:

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

    For x=14 the Z-score is:

    Z_{14}=\frac{14-16}{1}=-2

    For x=18 the Z-score is:

    Z_{18}=\frac{18-16}{1}=2

    Then we look for the percentage of the data that is between -2 <Z <2 deviations from the mean.

    According to the empirical rule 95% of the data is less than 2 standard deviations of the mean.  This means that 95% of students are between 14 and 18 years old

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