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    Z-score, Normal Probability & Percentiles

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    1. Consider the following scores comprising a population of size N = 14

    X F
    14 1
    13 2
    12 4
    11 3
    10 2
    9 2

    A. What is the mean for these N = 14 scores?
    B. What is the mode for these N = 14 scores?
    C. What is the standard deviation for these N = 14 scores?

    2. Using a mean of 7.55 and a standard deviation of 1.86, convert the following values of X into z-scores:
    A. X = 10.48, z =
    B. X = 3.17, z =
    C. X = 8.41, z =
    D. X = 5.62, z =

    3. Assuming a mean of 7.55 and a standard deviation of 1.86, what is the probability that:
    A. p(X > 10.48)
    B. p(X < 3.17)
    C. p(X < 8.41)
    D. p(X > 5.62)

    4. Assuming a normal distribution, what values of z corresponds to the following percentiles?
    A. 75th
    B. 25TH
    C. 40TH
    D. 60TH
    E. 50TH

    PLEASE SHOW ALL STEPS REQUIRED TO SOLVE EACH PROBLEM.

    © BrainMass Inc. brainmass.com October 10, 2019, 1:43 am ad1c9bdddf
    https://brainmass.com/statistics/probability/score-normal-probability-percentiles-346633

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    1. Consider the following scores comprising a population of size N = 14

    X F
    14 1
    13 2
    12 4
    11 3
    10 2
    9 2

    Answers

    X F X2 X * F X2 * F
    14 1 196 14 196
    13 2 169 26 338
    12 4 144 48 576
    11 3 121 33 363
    10 2 100 20 200
    9 2 81 18 162
    Total 14 159 1835

    A. What is the mean for these N = ...

    Solution Summary

    The solution provides step by step method for the calculation of z-score and probability using the Z score. Formula for the calculation is also included.

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