Solution:
Given:
[tex]\begin{gathered} \mu=100 \\ \sigma=15 \\ n=41 \\ x=99 \end{gathered}[/tex]
From the Z-scores formula;
[tex]\begin{gathered} Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}} \\ Z=\frac{99-100}{\frac{15}{\sqrt{41}}} \\ Z=-0.42687494916 \\ Z\approx-0.4269 \end{gathered}[/tex]
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
