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1. (10 points) True or False questions. Each is worth 2 points.
When comparing data, frequency distributions are more important than relative frequency
distributions.
When comparing data, relative frequency distributions are more important than frequency
distributions.
The probability distribution is calculated theoretically whereas the relative frequency distribution
is calculated experimentally.
The central limit theorem says that as the number of trials grows to infinity, the relative
frequency distribution approaches the probability distribution.

2. (10 points) A fair die is rolled, and the number on the top face is observed. Let X denote the
random variable of the number on the top face. Determine the probability distribution for X
and draw its histogram.

3. (10 points) Consider an urn with 6 blue balls and 2 red balls. A sample of three balls is chosen
at random from the urn. Let X denote the random variable of red balls in the sample. Find the
probability distribution of X and draw its histogram.

4. (10 points) An archer can hit the bull’s-eye of the target with probability 1/4. She shoots until
she hits the bull’s-eye or until give shots have been taken. Let X denote the random variable of
the number of shots taken. Determine the probability distribution for X and draw its histogram.

5. (10 points) Each time that a baseball player is at bat, the probability that he gets a hit is 0.35.
He comes up to bat four times in a game. Assume that his times at bat are independent trials.
Find the probability that he gets at least two hits.

6. (10 points) How many times must a person toss a fair coin so that the probability of obtaining
at least one head is greater than 0.95?

7. (10 points) A college student received grades 4,4,4,4,3,3,2,2,1 for three-credit courses and
4,4,4,3,3,2,2 for four-credit courses. What was her GPA?

8. (10 points) A committee of three people is to be selected at random from a country concil
consisting of five Democrats and four Republicans. What is the expected number of Democrats
on the committee?

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