Question

On a standard IQ test, the scores are normally distributed with a mean of 100 and a standard deviation of 20.

a) If you score 140, in which percentile are you?
b) If you score 90, in which percentile are you?

Answer 1

Explanation:

Since the scores of the standard IQ test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = IQ test scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 100

σ = 20

a) If you score 140, then

z = (140 - 100)/20 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

The percentile is 0.9 × 100 = 98

b) If you score 90, then

z = (90 - 100)/20 = - 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.31

The percentile is 0.31 × 100 = 31