application of the sampling distribution of x the GBAs of all students enrolled at  a large university have an approximately normal ditribution with a mean of 3.02 and a standard deviation of 0.29 ..find the probability that the mean GBA of a random sample of 20 student selected from this university is ,
a)3.10 or higher
b)2.90 or Lower
c)2.95 to 3.11

Imagine taking a random sample of $20$ students. Let random variables $X_1,X_2,\dots, X_{20}$ be their GBAs, and let $Y=\frac{1}{20}(X_1+X_2+\cdots+X_{20})$ be the sample mean.
Then $Y$ has (approximately) normal distribution, with mean $3.02$ and standard deviation $\dfrac{0.29}{\sqrt{20}}\approx 0.064846$. From here on we pretend $Y$ has exactly normal distribution, with mean $3.02$ and standard deviation $0.064846$. 
Then 
$$\Pr(Y\ge 3.10)=\Pr\left(Z\ge \frac{3.10-3.02}{0.064846}\right),$$
where $Z$ is standard normal.
Now we can find the required probability by using tables of the standard normal, or appropriate software.
The other questions are handled in a similar way.  
