1. A study of 204 advertising firms revealed their income after taxes:
|
Income after Taxes
|
Number of Firms
|
|
Under $1 million
|
104
|
|
$1 million to $20 million
|
54
|
|
$20 million or more
|
40
|
|
(a) What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)
(b-1) What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)
(b-2) What rule of probability could be applied?
2. A student is taking two courses, history and math. The probability the student will pass the history course is .51, and the probability of passing the math course is .68. The probability of passing both is .42.
What is the probability of passing at least one? (Round your answer to 2 decimal places.)
3. Solve the following:
(a) 30!/26!
(b) 10P6 =
(c) 9C6 =
The following information applies to the questions displayed below.]
4. Joe Mauer of the Minnesota Twins had the highest batting average in the 2009 Major League Baseball season. His average was .482. So assume the probability of getting a hit is .482 for each time he batted. In a particular game, assume he batted five times.
( a) This is an example of what type of probability?
5. (b) What is the probability of getting five hits in a particular game? (Round your answer to 3 decimal places.)
Calculate probabilities using the rules of multiplication.
6. There are 29 families living in the Willbrook Farms Development. Of these families 17 prepared their own federal income taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 5 by H&R Block.
(a) What is the probability of selecting a family that prepared their own taxes? (Round your answers to 3 decimal places.)
(b) What is the probability of selecting two families both of which prepared their own taxes?(Round your answers to 3 decimal places.)
(c) What is the probability of selecting three families, all of which prepared their own taxes? (Round your answers to 3 decimal places.)
(d) What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block? (Round your answers to 3 decimal places.)
Define the term conditional probability.
7. Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.)
|
X
|
P(X)
|
|
2
|
.1
|
|
4
|
.20
|
|
6
|
.30
|
|
8
|
.40
|
| |
06-03 Compute the mean of a probability distribution.
06-04 Compute the variance and standard deviation of a probability distribution.
8. Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 25 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 25 returns 5 had charitable contributions of more than $1,000. Suppose 4 of these returns are selected for a comprehensive audit.
(a) You should use the hypergeometric distribution because
(b) What is the probability exactly one of the four audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)
(c) What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.)
06-06 Describe and compute probabilities for a hypergeometric distribution.
9.An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 3.8 emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.
(a) What is the probability Linda Lahey, company president, received exactly 4 emails between 4 P.M. and 5 P.M. yesterday? (Round your answer to 4 decimal places.)
(b) What is the probability she received 6 or more emails during the same period? (Round your answer to 4 decimal places.)
(c) What is the probability she received two or less emails during the period? (Round your answer to 4 decimal places.)
10. A recent CBS News survey reported that 75 percent of adults felt the U.S. Treasury should continue making pennies.
Suppose we select a sample of 10 adults.
(a-1) How many of the 10 would we expect to indicate that the Treasury should continue making pennies? (Round your answer to 2 decimal places.)
(a-2) What is the standard deviation? (Round your answer to 4 decimal places.)
(b) What is the likelihood that exactly 7 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.)
(c) What is the likelihood at least 7 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.)
Objective: 06-05 Describe and compute probabilities for a binomial distribution.
11. In a binomial situation, n = 5 and .25. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.)
(a) x = 3
(b) x = 4
06-05 Describe and compute probabilities for a binomial distribution.
12. Refer to the following table.
|
First Event
|
|
|
|
|
|
|
Second Event
|
A1
|
A2
|
A3
|
Total
|
|
B1
|
3
|
4
|
5
|
12
|
|
B2
|
4
|
6
|
4
|
14
|
|
|
|
|
|
|
|
Total
|
7
|
10
|
9
|
26
|
|
|
|
|
|
|
| |
(a) Determine P(A1). (Round your answer to 2 decimal places.)
(b) Determine P(B1|A3). (Round your answer to 2 decimal places.)
(c) Determine P(B1 and A2). (Round your answer to 2 decimal places.)
05-07 Compute probabilities using a contingency table
13. The credit department of Lion's Department Store in Anaheim, California, reported that 20 percent of their sales are cash or check, 30 percent are paid with a credit card and 50 percent with a debit card. Twenty percent of the cash or check purchases, 80 percent of the credit card purchases, and 60 percent of the debit card purchases are for more than $50.
Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability she paid cash or check? (Round your answer to 3 decimal places.)
05-08 Calculate probabilities using Bayes theorem.
14. Which of these variables are discrete and which are continuous random variables?
(a) The number of new accounts established by a salesperson in a year.
(b) The time between customer arrivals to a bank ATM.
(c) The number of customers in Big Nick's barber shop.
(d) The amount of fuel in your car's gas tank.
(e) The number of minorities on a jury.
(f) The outside temperature today.
06-02 Distinguish between a discrete and a continuous random variable.
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.
| Number of days absent |
Probability |
| 0 |
0.6 |
| 1 |
0.2 |
| 2 |
0.12 |
| 3 |
0.04 |
| 4 |
0.04 |
| 5 |
0 |
What is the variance of the number of days absent?
Compute the variance and standard deviation of a probability distribution.