PLEASE HELP! I’m lost. :( In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math se

Question

PLEASE HELP! I’m lost. 🙁

In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean
µ = 520 and population standard deviation = 115.

What math SAT score is 1.5 standard deviations above the mean? Round answer to a whole number.

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Khải Quang 4 years 2021-08-14T16:23:51+00:00 1 Answers 39 views 0

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  1. Sapo1
    0
    2021-08-14T16:25:31+00:00
    Reply

    Answer:

    A math SAT score of 693 is 1.5 standard deviations above the mean

    Step-by-step explanation:

    Normal Probability Distribution

    Problems of normal distributions can be solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

    Mean µ = 520 and population standard deviation = 115.

    This means that \mu = 520, \sigma = 115

    What math SAT score is 1.5 standard deviations above the mean?

    This is X when Z = 1.5. So

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

    1.5 = \frac{X - 520}{115}

    X - 520 = 1.5*115

    X = 693

    A math SAT score of 693 is 1.5 standard deviations above the mean

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