Question

IQ scores are known to be normally distributed. The mean IQ score is 100 and the standard deviation is 15. The top 25% of the population (ranked by IQ score) have IQ’s above what value?

Answer 1

Answer:

110

Step-by-step explanation:

We have been given that the mean IQ score is 100 and the standard deviation is 15.

We will use normal distribution table to solve our given problem.

The top 25% of the population will represent scores greater than 75%.      

The z-score corresponding to data greater than 75% is 0.6745.

Upon substituting our given values in z-score formula, we will get:

$z=\frac{x-\mu}{\sigma}$

$0.6745=\frac{x-100}{15}$

$0.6745*15=\frac{x-100}{15}*15$

$10.1175=x-100$

$10.1175+100=x-100+100$

$110.1175=x$  

Therefore, the top 25% of the population (ranked by IQ score) have IQ’s above 110.