Statistics

Suppose that IQ scores have a bell-shaped distribution with a mean of 99 and a standard deviation of 12. Using the empirical rule, what percentage of IQ scores are less than 87? Please do not round your answer.

87-99 = -12/12 = -1

I get stuck here. I know 1 standard deviation lies between 68%.

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  1. 87 is 1 SD below mean. 68% are
    ±1 SD, therefore 34% are below the mean, leaving 50% - 34% = 16%

    Here is another way to figure it out exactly.

    Z = (score-mean)/SD

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100 to get percentage.

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  2. 16%

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