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Use the normal dist to approx the desired prob. Find the prob of getting at most 30 fives in 200 tosses of a fair 6 sided die

  • statistics -

    Mean = np
    SD = √npq

    n = 200
    p = 1/6
    q = 1 - p = 5/6

    Therefore:
    Mean = 200(1/6) = 33.33
    SD = √[200(1/6)(5/6)] = 5.27

    Use z-scores:
    z = (x - mean)/SD

    z = (30 - 33.33)/5.27 = -0.63

    Check a z-table for the probability.
    (Remember the problem is asking "at most 30" when looking at the table.)

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