What is the IQ score separating the bottom 20% from the top 80%?

Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Let X be the IQ scores for adults. Use the normal curve to explain your answer.

Answer 1

Ok, so to find the IQ score that separates the bottom 20 percent from the top 80 percent, we have to do a cumulative probability calculation in which we find the values up to the bottom 20 percent. So we will attack this problem by working backwards with our z-score. So we have to find z in which P(Z<z)=0.20. So come to find out, z=-0.84. We also know that to convert to z, we needed to know x-mean(x)/sd, and we have the mean and standard deviation. So:

-0.84=(X-100)/15

-12.6=X-100

87.4=X.

So the score of 87.4 is separating the bottom 20% from the top 80%.

Answer 2

I have already solved this problem for you.

Why do want to hear it again?

The answer is:

The z-score,z, such that Prob( Z < z) = 0.2 is z=-0.841621234

X = z*stndDev + mean

= -0.841621234 * 15 + 100

= 87.3756815

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https://www.wyzant.com/resources/answers/790973/what-is-the-iq-score-separating-the-bottom-20-from-the-top-80