statistics

of all 3-to 5-year- old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 250 will be enrolled in school.

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  1. Find mean and standard deviation. Use z-scores to find z, then a z-table to find your probability based on the z-score. This is a normal approximation to the binomial distribution.

    I'll get you started:

    mean = np = (500)(.56) = ?
    standard deviation = √npq = √(500)(.56)(.44) = ?
    Note: q = 1 - p

    Finish the calculations.
    To find z-score:
    z = (x - mean)/sd
    Note: x = 250

    Once you have the z-score, look in a z-table using the score to find your probability. Remember that the question is asking "at least 250" when looking at the table.

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  2. .243

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