Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person chosen at random will have an IQ score greater than 110?

Answer 1

We have the IQ as a normal random variable with a mean of 100 and a standard deviation of 5.

We have to calculate the probabiltiy of selecting a random person with an IQ greater than 110.

To do that we will:

• Calculate the z-score that correspond to X = 110.

,

• Use this z-score to find the probability in the standard normal distribution.

We can calculate the z-score for X = 110 as:

$z=\frac{X-\mu}{\sigma}=\frac{110-100}{5}=\frac{10}{5}=2$

Then, we can now look at the probability as:

$P(X>110)=P(z>2)\approx0.023$

Answer: the probability is approximately 0.023.