Answer in Statistics and Probability for kevu #251639

At a local high school, GPA’s are normally distributed with a mean of 2.5 and standard deviation of 0.6. What percentage of students at the high school have a GPA higher than 3.0?

Let “X” be a random variable representing the the GPA’s of students then, “X”~“N(mu, sigma^2)” where “mu=2.5” and “sigma^2=(0.6)^2.” Therefore, “X”~“N(2.5,0.6^2)”.

In order to determine the percentage of students who have a GPA higher than 3.0, we first find “p(Xgt3.0)”.

Now,

“p(Xgt3)=p((X-mu)/sigmagt(3-mu)/sigma)=p(Zgt(3-2.5)/0.6)=p(Zgt0.83)”

This can also be written as,

“p(Zgt 0.83)=1-p(Zlt0.83)=1-0.79673=0.20327”

The probability that students at the high school have a GPA higher than 3.0 is 0.20(2 decimal places).

Therefore, percentage of students who have a GPA higher than 3.0 is 0.20*100%=20%