Normal Distribution Question Approach

#1
Hello everyone,

first of all, this has nothing to do with coursework's or homework, I'm currently revising for an exam, so please help me.

Following question:

Grade point averages of students on a large campus follow a normal distribution with a mean 2.6 and a standard deviation of 0.5.

Question a asked for the probability of a student having 3.0 or more, which is 0.2119

Question b asked for the probability of a student being somewhere between 2.25 and 2.75, which is 0.3759.

Im fine with the methods of calculating that, but now it asks the following:


c) What is the minimum grade point average needed for a students grade point average to be among the highest 10 %?

d) A random sample of 400 students is chosen from the campus. What is the probability that at least 80 of these students have a grade point average above 3.0.

For this question i think that it is an approximation for a binomial distribution (which I'm familiar with), but i don't know how to do this specifically.




Thanks!!
 

Mean Joe

TS Contributor
#2
For c), you want to find (little) x such that P(X>x)=.10, where (big) X=a student's GPA. Need more help?

For d) define X=# of students with GPA above 3.0. In this problem, X is binomially distributed with n=400 and p=.2119 (from part a). This X has a mean and standard deviation (use your binomial distribution formulas). Then you calculate P(X>=80) = P(X>79.5) when we use the normal approximation. From here you calculate like part a).
 
#3
kay, got d), but don't get what you mean for c), can you try to explain that in terms of the normal distribution graph?

Thanks anyway, for the help so far
 

BGM

TS Contributor
#4
In question a) you are given a quantile, and asked for the related probability which you know how to solve it.

In question c) you are given a probability, and asked for the related quantile.

In terms of the graph of the pdf, now the given probability is the area under the curve from the point x to the positive infinity. As this area is given, try to find the cut-off point x (the quantile)