Respuesta :
Explanation:
We were given the following information:
This is a normal (bell-shaped) distribution having:
Mean = 2.54
Standard deviation = 0.41
x = 2.957
The empirical rule is a rule in statistics that states that almost all observed data will fall within three standard deviations of the mean, for a normal distribution.
We calculate the z-score as shown below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{2.957-2.54}{0.41} \\ z=\frac{0.417}{0.41} \\ z=1.017\approx1 \\ z=1 \end{gathered}[/tex]This means that 2.957 is about 1 standard deviation above the mean
Much more directly, the empirical rule predicts that 68% of observations falls within the first standard deviation, 95% within the first two standard deviations, and 99.7% within the first three standard deviations
To obtain the percentage of students having a GPA less than 2.957, we have:
[tex]\begin{gathered} =68+\frac{1}{2} \\ =68+0.5 \\ =68.5\text{ \%} \end{gathered}[/tex]Hence, 68.5% of the students have grade point averages less than 2.957
