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    Sampling Distribution of Sample Proportion

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    1) A store has determined that 25% of all sales are credit sales. A random sample of 75 sales is selected. What is the probability that the sample proportion will be:
    a) greater than .34?
    b) between .196 and .354?
    c) less than .25?
    d) less than .10?

    2) 10% of items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. What is the probability that the sample will contain:
    a) more than .025?
    b) less than .13 defective units?

    © BrainMass Inc. brainmass.com December 24, 2021, 9:42 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/sampling-distribution-sample-proportion-406061

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    Probability questions/need answers, but explanation of solution
    1) A store has determined that 25% of all sales are credit sales. A random sample of 75 sales is selected. What is the probability that the sample proportion will be:
    Answers
    Let X be the proportion of credit sales. Then X can be assumed to be normal with mean, µ = 0.25 and standard deviation σ = = = 0.05. Standardizing the variable X using and from standard normal tables, we can find the probabilities as follows.
    a) Greater than .34?
    P (X > 0.34) = = P (Z > 1.8) = 0.0359

    b) Between .196 and .354?
    P (0.196 < X < 0.354) =
    = P (-1.08 < Z < 2.08)
    = 0.8412

    c) Less than .25?
    P (X < 0.25) = = P (Z < 0) = 0.5000

    d) Less than .10?
    P (X < 0.10) = = P (Z < -3) = 0.00135

    2) 10% of items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. What is the probability that the sample will contain:
    Answers
    Let X be the defective items produced by the machine. Then X can be assumed to be normal with mean, µ = 0.10 and standard deviation σ = = = 0.03. Standardizing the variable X using and from standard normal tables, we can find the probabilities as follows.
    a) More than .025?
    P (X > 0.025) = = P (Z > -2.5) = 0.9938

    b) Less than .13 defective units?
    P (X < 0.13) = = P (Z < 1) = 0.8413

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:42 pm ad1c9bdddf>
    https://brainmass.com/statistics/probability/sampling-distribution-sample-proportion-406061

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