Question

IQ scores on the WAIS test approximate a normal curve with a mean of 100 and a standard deviation of 15. What IQ score is identified with the upper 2%

Answer 1

IQ scores of at least 130.81 are identified with the upper 2%.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 100 and a standard deviation of 15.

This means that
`\mu = 100, \sigma = 15`

What IQ score is identified with the upper 2%?

IQ scores of at least the 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.

`Z = (X - \mu)/(\sigma)`

`2.054 = (X - 100)/(15)`

`X - 100 = 15*2.054`

`X = 130.81`

IQ scores of at least 130.81 are identified with the upper 2%.