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    z value based probability problem

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    Question 1

    Convert x = 70 to z-score if Normal Distribution has mean = 50
    and Standard Deviation = 10.
    Answer

    0.5

    1.0

    1.5

    2.0

    Question 2

    Using the Appendix table for standard normal distribution find the area under the curve below z = -1.25
    Answer

    0.1432

    0.3461

    0.4574

    0.1056

    Question 3

    Find the are under standard normal distributon curve above z = 2.00
    Answer

    0.4572

    0.0228

    0.1462

    0.5431

    Question 4

    Use standard normal distribution table (Appendix Table II)
    to find the probability that z is between -1.5 and 1.5:
    P(-1.5 < z < 1.5)
    Answer

    0.9332

    0.4268

    0.8664

    0.0559

    Question 5

    For Normal distribution with mean 50 and standard deviation 10
    find probability that x will be below 35.
    Answer

    0.8893

    0.2101

    0.1020

    0.0668

    Question 6

    Household Income has Normal Distribution with average 44,000
    and Standard Deviation = 20,000. Find the probability that
    Household Income is GREATER than 56,000.
    Answer

    0.1245

    0.2743

    0.4184

    0.6105

    Question 7

    Number of students who graduate College every year is Normal Distribution
    with mean = 400 and standard deviation 50. Find probability that this year
    between 300 and 500 students will graduate College.

    Convert each number to z value and use Appendix tables B and C.
    Answer

    0.52

    0.65

    0.95

    0.81

    Question 8

    Sample size is 64, sample mean is 50.
    Assuming the population standard deviation is 16,
    construct 95.44% confidence interval for population mean.
    Factor z?/2=2
    Answer

    from 46 to 54

    from 40 to 60

    from 50 to 64

    from 35 to 65

    Question 9

    For sample mean x = 80, sample size n = 36 and sample standard deviation s = 24
    find 90% confidence interval for population mean.
    This is the case when population standard deviation is not known,
    you should use formula on page 328 with t-value from Appendix Table IV.
    Tip: For confidence level 90% ? = 1 - 0.90 = 0.10, ?/2 = 0.10/2 = 0.05
    In Table IV use column t0.05 and line with df = n - 1 = 36 - 1 = 35.
    Answer

    from 65.48 to 95.86

    from 75.44 to 82.16

    from 73.24 to 86.76

    from 70.18 to 88.65

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    https://brainmass.com/statistics/confidence-interval/z-value-based-probability-problem-462558

    Solution Preview

    Hi there,

    Thanks for your understanding. Here are my answers:

    Hi there,

    Thanks for allowing me to work on your questions.

    1. z=(x-mean)/standard deviation=(70-50)/10=2.

    2. find the area under the curve below z = -1.25
    Answer 0.1056

    3. Find the are under standard ...

    Solution Summary

    This solution provides some detailed explanation how to use z value to find out the probability.

    $2.19