# Assume that IQ scores are normally distributed, with a mean #mu# of 100 and standard deviation #sigma# of 15. What is the probability that a randomly selected person has an IQ score between 105 and 110?

##### 1 Answer

Jan 4, 2015

This question has already been answered. See the pasted answer below:

89.9

Because the data is defined to be normally distributed, the only information we need are the parameters, namely μ and σ.

Once we have these, we need to determine the value associated with the z-value at which the cumulative density function is equal to 0.25, meaning that 25% of values are less than that value.

You can solve using the Z-score formula, that is z=X−μσ.

By using a computer program or table, we can discover that

CDF−1(.25)=−.674.

Solving for X in the equation −.674=X−10015, X = 89.9.