a) To find the probability that the score is higher than 300 you have to find the Z-score for 300, by using the formula:

The probability of x>300 P(z>0)=1-P(z<=0)
Using the Standard Normal Cumulative Probability Table, P(z<=0)=0.5
Then,

Now, you can do the same to find the probability that the score is higher than 335, let' see:

The probability of x>335 is P(Z>1), then

These results mean that it is a 50% of probability that the score of the student chosen is greater than 300, and a 15.87% of probability that the score is greater than 335.
b) SRS=4, their mean score will be the same as the mean of the population = 300, the standard deviation of the sample is the standard deviation of the population divided by √n (n is the size of the sample=4).
![\mu=300\text{ and }\sigma=\frac{35}{\sqrt[]{4}}=17.5](https://img.qammunity.org/2023/formulas/mathematics/college/ojq7k24fkljv2mpq57csi44rmvq46wpnm3.png)
c) The probability that the mean score for the SRS is higher than 300 is:


The probability that the mean score for the SRS is higher than 335 is:


These results mean that it is a 50% of probability that the mean score of the SRS is greater than 300, and a 2.28% of probability that the mean score is greater than 335.