Candice is preparing for her final exam in Statistics. She knows she needs an 62 out of 100 to earn an A overall in the course. Her instruct

Question

Candice is preparing for her final exam in Statistics. She knows she needs an 62 out of 100 to earn an A overall in the course. Her instructor provided the following information to the students. On the final, 200 students have taken it with a mean score of 54 and a standard deviation of 6. Assume the distribution of scores is bell-shaped. Calculate to see if a score of 62 is within one standard deviation of the mean.

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Latifah 2 months 2021-07-22T18:43:33+00:00 1 Answers 3 views 0

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    2021-07-22T18:45:32+00:00

    Answer:

    A score of 62 is not within one standard deviation of the mean.

    Step-by-step explanation:

    When the distribution is normal, we use 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.

    Mean score of 54 and a standard deviation of 6.

    This means that \mu = 54, \sigma = 6

    Calculate to see if a score of 62 is within one standard deviation of the mean.

    Is Z between -1 and 1 when X = 62?

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

    Z = \frac{62 - 54}{6}

    Z = 1.33

    So a score of 62 is not within one standard deviation of the mean.

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