For the past ten years, grades on the final exam in Mr. Statman’s statistic course have been normally distributed with a mean of µ = 75 and a standard deviation of σ = 15. Mr. Statman has a current class with 50 students. Let us predict some outcomes on the final exam for that class. a) Draw a normal distribution. Include the mean and two standard deviations. Complete this sentence using the Empirical Rule: Approximately, 95% of students will score between and on the final exam.

b) Shade in the A range (90 and above) on your distribution in part a. Find the probability that a randomly selected student makes an A on Mr. Statman’s final exam. How many of the 50 students do we expect to make an A?

c) Suppose that we randomly select 5 students from the class and AVERAGE their final exam scores. The Central Limit Theorem indicate that the average of the 5 students will fall somewhere in a Normal Distribution with = and = . Complete this sentence using the Empirical Rule: Approximately, 95% of the time the average of 5 random students will fall between and on the final exam.

d) Find the probability that the average of the 5 students is an A average (90 and above).

e) Let’s do the same thing that we did in parts c and d, except for the entire class of 50. The Central Limit Theorem indicate that the average of the 50 students will fall somewhere in a Normal Distribution with = and = . Complete this sentence using the Empirical Rule: Approximately, 95% of the time the average of 50 random students will fall between and on the final exam.

f) Find the probability that the average of the 50 students is an A average (90 and above).

g) Find the following probabilities (you redoing parts b, d, and f, but with a C instead of an A) :

A) P(a randomly selected student makes a C on the final exam) =

B) P(a sample of 5 randomly selected students make a C average of the final exam) =

C) P(the class average of all 50 students will be a C average)

h) Discuss what you have learned from this exercise.