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

The given parameters in the question is:

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

Calculating the z sore gives:

`\begin{gathered} z=(x-\mu)/((\sigma)/(√(n)))=(96-100)/((15)/(√(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`