Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If a certain statistician has an IQ of 122, what percent of the population has an IQ less than she does?

A. 7%
B. 22%
C. 93%
D. 99%
E. 47%

Answer 1

93% of the population has an IQ less than she does

Explanation:

Mean =
`\mu = 100`

Standard deviation =
`\sigma = 15`

x = 122

Formula :
`z= (x-\mu)/(\sigma)`

`z= (122-100)/(15)`

`z=1.46`

Refer the z table for p value

So, p value = 0.9279

Percentage = 92.7% ≈ 93%

So, 93% of the population has an IQ less than she does

Answer 2

z = ( 122-100 ) / 15 = 22/15 = 1.467
Then we have to use a z-table for a normal distribution.
The percent of the population that has an IQ less than she does is C ) 93%