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According to the book Are you Normal?,40% of all US adults try to pad their auto insurance claims to cover their deductible. Your office has just received 128 in insurance claims to be processed in the next few days, what is the probability that fewer than 45 of the claims have been padded? Round your answer to the nearest thousandths place.

  • statistics -

    Use the normal approximation to the binomial distribution.

    Mean = np = 128 * .40 = 51.2
    Standard deviation = √npq = √(128 * .40 * .60) = √30.72 = 5.54

    Note: q = 1 - p

    Formula for z-scores:
    z = (x - mean)/sd

    With your data:
    z = (45 - 51.2)/5.54 = -1.12

    Look at a z-table for the probability using the z-score.

    Double check my calculations.

    I hope this will help.

  • statistics -

    the answer is 0.113 its confusing and i got it wrong the first time too, (same class)

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