Question

A particular IQ test is standardized to a Normal model, with a mean of 80 and a standard deviation of 12.

Using the Empirical rule determine about what percent of people should have IQ scores less than 44?

The percent of people with IQ scores less than 44 is:

Answer 1

A particular IQ test is standardized to a Normal model with $\mu = 80, \sigma=12$

The proportion of people with IQ scores less than 44 is: $P(Z<\frac{44-80}{12})=P(Z<-3)$

the empirical rule predicts that 68% of observations falls between the first standard deviation.

95% between the first two standard deviations.

and 99.7% between the first three standard deviations.

Normal distribution is symmetric, outside the 3 standard deviation the proportion is 1-0.997 = 0.003

Toward the left tail that is

0.003 P(Z <-3) 0.0015 2

The percent of people with IQ scores less than 44 is: 0.15%