Name: ____________________________________
Chapter 5 Review – Probability Distributions, Mean, Variance, Standard Deviation, Binomial Distributions
Section 5.1 – Probability Distributions, Graphs, Types of Variables
1. (5.1) What are examples of continuous variables? What are examples of discrete variables?
2.
a.
(5.1) Determine whether the distribution represents a probability distribution. If it does not, state why.
X
1
2
3
4
P(x) 1/10 3/10 1/10 2/10
5
3/10
b.
X
P(X)
5
0.3
10
0.4
15
0.1
X
P(X)
8
12
16
20
5/6 1/12 1/12 1/12
c.
3. (5.1) The number of emergency calls a local police department receives per 24-hour period is distributed
as shown here. Construct a graph for the data.
Number of calls X
P(X)
10
11
12
13
14
0.02 0.12 0.40 0.31 0.15
4. (5.1) Construct a probability distribution for the following graph.
5. (5.1) A box contains 5 pennies, 3 dimes, 1 quarter, and 1 half-dollar. Construct a probability
distribution and draw a graph for the data.
Section 5.2 – Mean, Variance, Standard Deviation, Expected Value of a Probability Distribution
1.
(5.2) A large retail company encourages its employees to get customers to apply for the store credit
card. Below is the distribution for the number of credit card applications received per employee for an
8-hour shift.
X
0
1
2
3
4
5
P(X) 0.27 0.28 0.20 0.15 0.08 0.02
a. What is the probability that an employee will get 2 or 3 applications during any given shift?
b. Find the mean, variance, and standard deviation for this probability distribution.
2.
(5.2) You draw one card from a standard deck of playing cards. If you pick a heart, you will win $10.
If you pick a face card, which is not a heart, you win $8. If you pick any other card, you lose $6. Do you
want to play? Explain.
3. (5.2) A manufacturer is considering the manufacture of a new and better mousetrap. She
estimates the probability that the new mousetrap is successful is 3/4. If it is successful it
would generate profits of $120,000. The development costs for the mousetrap are $98,000.
Should the manufacturer proceed with plans for the new mousetrap? Why or why not?
4. (5.2) A grab bag contains 12 packages worth 80 cents apiece, 15 packages worth 40 cents apiece and 25
packages worth 30 cents apiece. Is it worthwhile to pay 50 cents for the privilege of picking one of the packages
at random?
.
Section 5.3 – Binomial Distributions – Probability, Mean, Variance, Standard Deviation
1. (5.3) Use the binomial table to answer the question. A fair coin is flipped six times and the number of
heads is counted. Calculate the probability that the coin will land heads more than four times.
2. (5.3) Fourteen percent of cell phone users use their cell phones to access the Internet. In a random sample of
10 cell phone users, what is the probability that exactly 2 have used their phones to access the? More than 2?
3. (5.3) If 80% of job applicants are able to pass a computer literacy test, find the mean, variance, and standard
deviation of the number of people who pass the examination in a sample of 150 applicants.
4. (5.3) Three out of four American adults under age 35 have eaten pizza for breakfast. If a random sample of
20 adults under age 35 is selected, find the probability that exactly 16 have eaten pizza for breakfast.
5. (5.3) If 4% of the population carries a certain genetic trait, find the probability that in a sample of 100 people,
there are exactly 8 people who have the trait.
6. (5.3) If five cards are drawn from a deck, find the probability that two will be hearts?
7. (5.3) In a survey, 65% of the voters support a particular referendum. If 30 voters are chosen at random, find
the mean, variance, and standard deviation for the number of voters who support the referendum.
8. (5.3) A student takes a 6 question multiple choice quiz with 4 choices for each question. If the student
guesses at random on each question, what is the probability that the student gets exactly 4 questions correct?
9. (5.3) Use the Binomial table to answer the question. A pet supplier has a stock of parakeets of which 30%
are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at
random, what is the chance that the pet store gets exactly one blue parakeet?