Mean = 80
St Dev = 8
We take this as a normal distribution question.
First, the 68-95-99 rule.
The normal distribution is commonly associated with the 68-95-99 rule.
• 68% of the data is within 1 standard deviation (σ) of the mean (μ),
,• 95% of the data is within 2 standard deviations (σ) of the mean (μ),
,• and 99 of the data is within 3 standard deviations (σ) of the mean (μ).
Checking the two scores, it doesnt fall between any of the rules, so we need to convert to z scores.
The formula is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]The first score (x) is 76, so corresponding z score is:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{76-80}{8}=-.5 \end{gathered}[/tex]The second score is 94, this corresponds to:
[tex]z=\frac{94-80}{8}=1.75[/tex]This is:
We want the proportion (percentage).
Which is the blue shaded region.
If we use a normal table, we need:
z(1.75) - z(-0.5)
0.4599+0.1915 = 0.6514
In percentage, that is:
0.6514 * 100 = 65.14%
Hence, 65.14% of individuals would score between Pat and Chris.
