Question

A random sample of 41 people is taken. What is the probability that the main IQ score of people in the sample is less than 99? Round your answer to four decimal places if necessary(See picture )

Answer 1

Given:

`\begin{gathered} \mu=100 \\ \sigma=15 \\ n=41 \\ x=99 \end{gathered}`

From the Z-scores formula;

`\begin{gathered} Z=(x-\mu)/((\sigma)/(√(n))) \\ Z=(99-100)/((15)/(√(41))) \\ Z=-0.42687494916 \\ Z\approx-0.4269 \end{gathered}`

From Z-scores table, the probability that the mean IQ score of people in the sample is less than 99 is;

[tex]\begin{gathered} P(x

Therefore, to 4 decimal places, the probability that the mean IQ score of people in the sample is less than 99 is 0.3347