Question

Scores on a standard IQ test are normally distributed with a mean of 100 and

a standard deviation of 15. To the nearest integer value, how high must your
IQ be to fall within the top 5% of scores?
OA. 128
OB. 124
OC. 127
OD. 126
OE. 125

Answer 1

To find the IQ score that falls within the top 5% of scores, we need to determine the z-score corresponding to the 95th percentile.

Since the normal distribution is symmetric, the 95th percentile is equivalent to the z-score that leaves 5% in the tail on the right side.

Using a standard normal distribution table or a calculator, we find that the z-score for the 95th percentile is approximately 1.645.

To find the IQ score, we can use the z-score formula:

z = (x - μ) / σ

Rearranging the formula to solve for x (IQ score), we have:

x = z * σ + μ

Plugging in the values, we have:

x = 1.645 * 15 + 100

x ≈ 124.68

Rounding to the nearest integer, the IQ score required to fall within the top 5% of scores is 125.

Therefore, the correct answer is OE. 125.