The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.

Question

The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points. About what percent of students have scored less than 45 points?

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Everleigh 2 weeks 2021-09-15T03:22:10+00:00 1 Answer 0

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    2021-09-15T03:23:14+00:00

    Answer:

    0.13% of students have scored less than 45 points

    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 = 60, \sigma = 5

    About what percent of students have scored less than 45 points?

    This is the pvalue of Z when X = 45. So

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

    Z = \frac{45 - 60}{5}

    Z = -3

    Z = -3 has a pvalue of 0.0013

    0.13% of students have scored less than 45 points

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