GIVEN:
We are given that IQ scores have a bell shaped distribution with a mean of 96 and a standard deviation of 17.
Required;
Using the emperical rule, what percentage of IQ scores are no more than 79?
Step-by-step explanation;
For a bell-shaped distribution, we already know that,
68% of the data set lies within one standard deviation
95% of the data set lies within two standard deviations
99.7% of the data set lies within three standard deviations
The condition given is that the IQ scores are no more than 79, hence;
[tex]\begin{gathered} n=\frac{79-96}{17} \\ \\ n=\frac{-17}{17}=-1 \end{gathered}[/tex]
Now we can see that the IQ score of 79 is 1 standard deviation to the left of the mean (that is to the left of 96).
We also take note that 68% of the data set lies within one standard deviation on either side of the mean.
Therefore, for the IQ scores to be 1 standard deviation from the mean, we would have;
[tex]\begin{gathered} \frac{1-68\%}{2}=\frac{1-0.68}{2} \\ \\ =0.16 \end{gathered}[/tex]
Expressed as a percentage, we now have
[tex]1.6\%[/tex]
ANSWER:
Therefore, 1.6% of IQ scores would be no more than 79.
