Question

Intelligence quotient scores are often reported to be normally distributed with( see picture) A random sample of 43 people is taken. What is the probability of a random person on the street having an IQ score of less than 96? Round your answer to four decimal places if necessary

Answer 1

SOLUTION

The given parameters in the question is:

$\mu=100,\sigma=15,X=96$

Calculating the z sore gives:

$\begin{gathered} z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{96-100}{\frac{15}{\sqrt{43}}} \\ z=-1.749 \end{gathered}$

The required probability is:

$P(x>z)=P(x>-1.749)$

Using a z sore calculator, the required answer is:

$P(x<96)=0.04015$