Suppose that the scores of a history test are normally distributed with a mean of 565 and a standard deviation of 113. a) What percentage of

Question

Suppose that the scores of a history test are normally distributed with a mean of 565 and a standard deviation of 113. a) What percentage of the scores are less than 450?

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Athena 2 weeks 2021-10-03T11:38:18+00:00 1 Answer 0

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    2021-10-03T11:39:37+00:00

    Answer:

    15.39% of the scores are less than 450

    Step-by-step explanation:

    Problems of normally distributed samples are 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 = 565, \sigma = 113

    What percentage of the scores are less than 450?

    This is the pvalue of Z when X = 450. So

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

    Z = \frac{450 - 565}{113}

    Z = -1.02

    Z = -1.02 has a pvalue of 0.1539

    15.39% of the scores are less than 450

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