# You happen to know that the average GPA (grade point average)

August 30, 2017

Question
Question 1

You happen to know that the average GPA (grade point average) for the 5,000 sophomores at USC is 2.8 with a population standard deviation of .25. Amazingly, the GPAs are normally distributed. If you take a random sample of 40 sophomores, what is the probability that the average gpa will be more than 2.9?

.0057

.7257

.9943

.2743

Question 2

You happen to know that the average GPA for the 5,000 sophomores at USC is 2.8 with a population standard deviation of .25. Amazingly, the GPAs are normally distributed. If you take a randomly chosen sophomore, what is the probability that her gpa will be less than 2.9?

.0057

.3446

.9943

.6554

Question 3

A lumber manufacturer sells framing lumber. The length of their boards are normally distributed and average 8 ft long with a standard deviation of .04 ft. What are the odds that if you took a sample of 50 boards that their average would be less than 8.015 ft?

.0040

2.66

.6462

.9960

Question 4

You happen to know that the average GPA (grade point average) for the 5,000 sophomores at USC is 2.8 with a population standard deviation of .25. If you take a sample of 30 sophomores, there is a ten percent chance the sample average will be less than what value?

2.48

2.742

1.282

2.858

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