Prompt According to the College Board website, the scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and standar

Question

Prompt According to the College Board website, the scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and standard deviation of 111. Assume that SAT-M scores have a normal probability distribution. One of the criteria for admission to a certain engineering school is an SAT-M score in the 98th percentile. This means the score is in the top 2% of scores. Find the actual SAT-M score marking the 98th percentile?

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2 weeks 2021-09-11T22:05:58+00:00 1 Answer 0

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    2021-09-11T22:07:38+00:00

    Answer:

    The actual SAT-M score marking the 98th percentile is 735.105.

    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 = 507, \sigma = 111

    Find the actual SAT-M score marking the 98th percentile?

    This is the value of X when Z has a pvalue of 0.98. So it is X when Z = 2.055.

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

    2.055 = \frac{X - 507}{111}

    X - 507 = 2.055*111

    X = 735.105

    The actual SAT-M score marking the 98th percentile is 735.105.

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