# Determining random variables

1. For each of the experiments described, let x determine a random variable and use your knowledge of probability to prepare a probability distribution . Use a tree diagram.

Two dice are rolled and the total number of points is recorded.

2. According to the Web site of Mars, the makers of M&M'S plain chocolate candies, 21%of the candies produced are green. If we select 4 candies from a bag at random and record the number of green candies, the probability distribution is as follows. Find the expected value for the number of green candies

X 0 1 2 3 4

P(X) .3895 .4141 .1651 .0293 .0019

3. During the month of July, a home improvement store sold a great many air conditioning units, but some were returned .The following table shows the probability distribution for the daily number of returns of air conditioning units sold in July. Find the expected number of returns per day

X 0 1 2 3 4 5

P(x) .55 .31 .08 .04 .01 .01

4. According to Len Pasquarelli, in the first 10 games of the 2004 professional football season in the US two point conversations were successful 51.2% of the time. We can compare this rate with the historical success rate of extra-point kicks of 94%.

a. Calculate the expected value of each strategy

b. Over the long run, which strategy will maximize the number of points scored?

c. From this information, should a team always use only one strategy?

5. Researchers at the London University estimated that 34% of the mortgage foreclosures that occurred in the United States in 2008 were in the state of California. If 15 foreclosed mortgages were selected at random, find the probability that:

a. None was from California

b. Exactly 10 were not from California

6. The study from the National Federation of independent business also found that approximately 56% of small businesses choose the cost of health care as the number one challenge facing their business. If we select 8 small businesses at random, find the probability that the given number of businesses chose the cost of health care as the number-one challenge:

a. All 8 businesses

b. At Most 2 businesses

#### Solution Preview

Section 9.1: 2, 24, 36, 42

1

For each of the experiments described , let x determine a random variable and use your knowledge of probability to prepare a probability distribution . Use a tree diagram

Two dice are rolled and the total number of points is recorded.

This an example for first dice with number 1, the second dice could have 1 to 6.

For the rest, we just change the first number from 2 to 6.

Based on the tree diagram, we could have the following distribution.

x P(x)

2 1/36

3 1/18

4 1/12

5 1/9

6 5/36

7 1/6

8 5/36

9 1/9

10 1/12

11 1/18

12 1/36

2

According to the Web site of Mars, the makers of M&M'S Plain chocolate candies, 21%ofthe candies produced and green. If we select 4 candies from a bag at random and record the number of green candies, the probability distribution is ...

#### Solution Summary

The expert determines random variables for beginner statistics.