If we were to take the average of the 35 students’ scores, what is the probability that their average would be higher than 1150?

For a study, 5 high school seniors’ names are chosen in a random drawing. Their SAT scores are: 1100, 1200, 900, 1250 and 950.

Mean is 1080

Standard deviation is 136.38

Answer the questions below:

Question #1:  Let’s assume that nationwide individual scores follow a Normal Distribution with the mean of 1100 and a standard deviation of 150. What percentage of individual students would you expect to get a score of 1150 or higher?

Question #2:  Let’s say that we sample 35 students from another school which is your typical American school (same individual mean and standard deviation as d above). If we were to take the average of the 35 students’ scores, what is the probability that their average would be higher than 1150?