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29 June, 15:32

The scores of high school seniors on the act college entrance examination in a recent year had mean μ = 20.8 and standard deviation Ï = 4.8. the distribution of scores is only roughly normal. (a) what is the approximate probability that a single student randomly chosen from all those taking the test scores 21 or higher? (r

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  1. 29 June, 19:28
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    To solve this problem, we make use of the z statistic. The formula for z score is:

    z = (x - μ) / s

    where,

    x = is the sample score = 21 or higher

    μ = the population mean = 20.8

    s = the standard deviation = 4.8

    Solving for the z score:

    z = (21 - 20.8) / 4.8

    z = 0.0417

    Next step to do is to find for the p value using the standard distribution tables at z = 0.04. Since we are looking for the probability of getting 21 or higher, therefore this is a right tailed test, hence

    p = 0.516

    So there is about 51.6% that a student will get a score of 21 or greater.
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