In 2017, 1,764,865 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ = 467 and a standard

Question

In 2017, 1,764,865 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ = 467 and a standard deviation σ = 111. Let X = a SAT exam verbal section score in 2017. Then X ~ N(467, 111). Find the z-scores for x1 = 235 and x2 = 368.

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1 week 2021-11-19T09:57:47+00:00 1 Answer 0 views 0

Answers ( )

  1. Emma
    0
    2021-11-19T09:58:55+00:00

    Answer:

    X1 zscore

    Z = -2.09

    X2 zscore

    Z = -0.89

    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 = 467, \sigma = 111

    x1 = 235

    Z when X = 235

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

    Z = \frac{235 - 467}{111}

    Z = -2.09

    x2 = 368.

    Z when X = 368

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

    Z = \frac{368 - 467}{111}

    Z = -0.89

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