Each year about 1500 students take the introductory statistics course at a large university. This year scores on the final exam are distributed with a median of 74 points, a mean of 70 points, and a standard deviation of 10 points. There are no students who scored above 100 (the maximum score attainable on the final) but a few students scored below 20 points.
(a) Is the distribution of scores on this final exam symmetric, right skewed, or left skewed?
(b) Would you expect most students to have scored above or below 70 points?
(c) Can we calculate the probability that a randomly chosen student scored above 75 using the normal distribution?
(d) What is the probability that the average score for a random sample of 40 students is above 75?
(e) How would cutting the sample size in half affect the standard error of the mean?