Question

Given IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, the proportion of people with IQs above 130 is

Answer 1

The proportion of people with IQs above 130 is 2.3%.

How to calculate the value?

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Here the mean is 100 and a standard deviation of 15.

µ = 100, σ = 15

P(X > 130) =

= P( (X-µ)/σ > (130-100)/15)

= P(z > 2)

= 1 - P(z < 2)

Using excel function:

= 1 - NORM.S.DIST(2, 1)

= 0.023 = 2.3%

The value is 2.3%.

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