1) the Mass Function of a Random Variable X Is Given Below

Chapter 5 Review

1. The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph.

2. The number of song requests a radio station receives per day is indicated in the table below. Construct a graph for this data. Number of calls, x 8 9 10 11 12 Probability ,p(x) 0.21 0.31 0.16 0.14 0.18

3. For the following data, construct a graph showing the probability distribution. x p(x) 0 0.35 1 0.25 2 0.20 3 0.15 4 0.05

4. Why is the following distribution is not a probability distribution? x -5 -4 -3 -2 -1 P(x) 0.19 0.16 –0.10 0.48 0.27

5. What of the following pairs of probability values would complete the following probability distribution? x -3 -2 -1 0 1 2 P(x) 0.09 0.21 p1 p2 0.17 0.25

6. A multiple choice quiz consists of 7 questions, each with 3 possible answers. If a student guesses at the answer to each question, then the mean number of correct answers is what?

Chapter 5 Review

7. What probability value would be needed to complete the following probability distribution? x -5 -1 0 1 4 P(x) 0.12 0.24 0.12 0.24

8. Find the mean and standard deviation of the distribution shown. x -3 -2 -1 0 P(x) 0.20 0.24 0.47 0.09

Chapter 5 Review

Answer Key

4. A probability is negative 5. p1= 0.02, p2 = 0.26 6. 2.33 7. 0.28 8. –1.55

Chapter 5 Review

Additional Questions:

1) The mass function of a random variable X is given below

Value of X 1 1.5 2 3 P(X=x) 0.4 0.4 0.1

a. Complete the table.

b. Find the expected value of X.

c. What is the probability of getting at least a two?

d. Find the standard deviation of the random variable X.

2) A box contains two $1 bills, three $5 bills, one $10 bill, and three $20 bills. Construct a probability distribution for the data.

3) A bank vice president feels that each savings account customer has, on average, three credit cards. The following distribution represents the number of credit cards people own. Find the mean, variance, and standard deviation. Is the vice president correct?

4) A pizza shop owner determines the number of pizzas that are delivered each day. Find the mean, variance, and standard deviation for the distribution shown. If the manager stated that 45 pizzas were delivered on one day, do you think that this is a believable claim?

5) A 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $360. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999057. Find the expected value of the policy for the insurance company.