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11 November, 05:57

Iq scores are normally distributed with a mean of 100 and a standard deviation of 15 if one person is randomly selected what is the probability that the persons IQ falls between 110 and 130

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  1. 11 November, 06:24
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    probability that the persons IQ falls between 110 and 130 is 0.2286.

    Step-by-step explanation:

    Step 1: Sketch the curve.

    The probability that 110
    Step 2:

    Since μ=100 and σ=15 we have:

    P (110 < X < 130) = P (110-100 < X-μ < 130-100)

    ⇒ P ((110-100) / 15< (X-μ) / σ< (130-100) / 15)

    Since Z = (x-μ) / σ, (110-100) / 15 = 0.67 and (130-100) / 15 = 2 we have:

    P (110
    Step 3: Use the standard normal table to conclude that:

    P (0.67
    Therefore, probability that the persons IQ falls between 110 and 130 is 0.2286.
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