A class is given an exam. The distribution of the scores is normal. The mean score is 76 and the standard deviation is 11. Determine the tes

Question

A class is given an exam. The distribution of the scores is normal. The mean score is 76 and the standard deviation is 11. Determine the test score, c c , such that the probability of a student having a score greater than c c is 36 % 36% . P ( x > c )

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RobertKer 3 years 2021-09-05T16:59:42+00:00 1 Answers 26 views 0

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  1. linhdan
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    2021-09-05T17:01:04+00:00
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    Answer: required value of c = 79.94.

    Step-by-step explanation:

    Let x denotes the exam score.

    Given: The mean score is 76 and the standard deviation is 11.

    to detrmine c , such that the probability of a student having a score greater than c  is 36 %.

    or P(x>c)=0.36

    Using z-score table , we get

    z= 0.3584 [z-value corresponds to p-value of 0.36(one-tailed) is 0.3584]

    Formula for z:

    z=\dfrac{x-mean}{standard\ deviation}\\\\ 0.3584=\dfrac{c-76}{11}\\\\ c=0.3584\times11+76\\\\ c=76+3.9424\\\\ c\approx 79.94

    hence, required value of c = 79.94.

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