Question

Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 61 people is taken.What is the probability that the mean IQ score of people in the sample is less than 98? Round your answer to 4 decimal places, if necessary.

Answer 1

To find the probability that the mean IQ score of people in the sample is less than 98, first we need to convert the value into z-score by using the formula:

`z=(x-\mu)/(\sigma)`

Then, when x=98:

`\begin{gathered} z=(98-100.0)/(15.0) \\ z=(-2.0)/(15.0) \\ z=-0.1333 \end{gathered}`

By checking in a standard normal table z=-0.1333 has a p-value=0.4471.

Then the probability is 0.4471 that also can be expressed as 44.71%