The number of calories burned at the gym is normally distributed with a mean of 425 and a standard deviation of 51. Find the Z-score for eac

Question

The number of calories burned at the gym is normally distributed with a mean of 425 and a standard deviation of 51. Find the Z-score for each data value.
a.)268 b.)512 c.)450

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Katherine 1 week 2021-11-25T02:23:00+00:00 1 Answer 0

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    2021-11-25T02:24:55+00:00

    Answer:

    (a) -3.708

    (b) 1.706

    (c) 0.490

    Step-by-step explanation:

    The z-score of normal distribution is given as:

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

    (a)

    Given:

    Score is, x=268

    Mean value is, \mu =425

    Standard deviation is, \sigma = 51

    z-score is, z=\frac{268-425}{51}=\frac{-157}{51}=-3.078

    (b)

    Given:

    Score is, x=512

    Mean value is, \mu =425

    Standard deviation is, \sigma = 51

    z-score is, z=\frac{512-425}{51}=\frac{87}{51}=1.706

    (c)

    Given:

    Score is, x=450

    Mean value is, \mu =425

    Standard deviation is, \sigma = 51

    z-score is, z=\frac{450-425}{51}=\frac{25}{51}=0.490

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