Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 103 and a standard deviation of 13. Describe where the highest and lowest 5 % of IQ scores lie. between 77 and 129 below 64 and above 142 below 77 and above 129 below 90 and above 116

Answer 1

This is a normal distribution question.

The empirical formula say:

Empirical Formula/Rule:

When you use a standard normal distribution (aka Gaussian Distribution):

0. About 68% of values fall within one standard deviation of the mean.

,

1. About 95% of the values fall within two standard deviations from the mean.

,

2. Almost all of the values—about 99.7%—fall within three standard deviations from the mean.

We are looking for 95th percentile and 5th.

So, we can take 95th percentile both sides.

We can use Rule #2 above:

2 standard deviations is 2 * 13 = 26

To both sides of mean (103), we have:

103 + 26 = 129

103 - 26 = 77

The answer is

below 77 and above 129 (third choice)