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8 January, 15:07

In a large population of college-educated adults, the mean iq is 112 with standard deviation 25. suppose 300 adults from this population are randomly selected for a market research campaign. the probability that the sample mean iq is greater than 115 is:

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  1. 8 January, 16:50
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    Given:

    μ = 112, population mean

    σ = 25, population std. deviation

    The randomly selected sample population of 300 (>30) is large enough for probability testing based on the normal distribution.

    x = 115, random variable.

    z-score:

    x = (x-μ) / σ = (115 - 112) / 25 = 0.12

    Let xs = sample mean.

    From standard tables, obtain

    P (xs<115) = 0.548

    Therefore

    P (xs>115) = 1 - 0.548 = 0.452 = 45% (approx)

    Answer: 45%
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