A set of data values is normally distributed with a mean of 90 and a standard deviation of 4. Give the standard score and approximate percen

Question

A set of data values is normally distributed with a mean of 90 and a standard deviation of 4. Give the standard score and approximate percentile for a data value of 89.

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Evelyn 16 hours 2021-10-12T11:51:41+00:00 1 Answer 0

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    2021-10-12T11:53:05+00:00

    Answer:

    Standard score of -0.25.

    A data value of 89 is approximately in the 40th percentile.

    Step-by-step explanation:

    Problems of normally distributed samples can be solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    In this problem, we have that:

    \mu = 90, \sigma = 4

    Give the standard score and approximate percentile for a data value of 89.

    Z when X = 89

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

    Z = \frac{89 - 90}{4}

    Z = -0.25

    Z = -0.25 has a pvalue of 0.4013.

    So a data value of 89 is approximately in the 40th percentile.

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45:7+7-4:2-5:5*4+35:2 =? ( )