Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.522.52 and a standard deviation of 0.420.42. using the empirical rule, what percentage of the students have grade point averages that are no more than 3.363.36? please do not round your answer.

Answer 1

Solution: We are given that the grade point average of undergraduate students at one university have a normal distribution, with mean, $\mu=2.52$ standard deviation,$\sigma=0.42$

We have to find the percentage of the students whose grade point averages are no more than 3.36, i.e., P(x<3.36).

We need to first find the z-score.

$z=\frac{x-\mu}{\sigma}$

 $=\frac{3.36-2.52}{0.42}$

 $=\frac{0.84}{0.42}=2$

Now we have to find $P(z$. Using the empirical rule, we know that 97.5% data lies below 2 standard deviations above mean.

Therefore, using the empirical rule, 97.5% of the students have grade point averages that are no more than 3.36.