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# Georgia Military College The Empirical Rule Exam Practice

Georgia Military College The Empirical Rule Exam Practice.

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.

Respond too two peer

Georgia Military College The Empirical Rule Exam Practice

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