Question

Given IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15, the proportion of people with IQs above 130 is:

Answer 1

Answer: 0.0228 .

Step-by-step explanation:

Given, IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15

Let X denotes the IQ score.

Then, the proportion of people with IQs above 130 is

$P(X>130)=P(\dfrac{X-mean}{ standard\ deviation}>\dfrac{130-100}{15})\\\\= P(Z>2)\ \ \ \[Z=\dfrac{X-mean}{ standard\ deviation}]$

$=1-P(Zz)=1-P(Z$

Hence, the proportion of people with IQs above 130 is 0.0228 .