IQ scores are standardized to produce a normal distribution with a mean of µ = 100 and a standard deviation of σ = 15. Find the proportion of the population in the following IQ category: Genius or near genius: IQ greater than 140.

Explanation:

First let's note* the given values:

Ζ = Χ - μ / σ

μ = 100;

σ = 15

Converting z score to a decimal P using the percentage-finding method you want.

a. Genius or near genius: IQ over 140  

z > 40 / 15 = 2.6667 P(z > 2.6667) = .0038  3.8% of whole the population

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explanation:

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