1. A study of 198 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. Refer to the following table.
|
First Event
|
|
|
|
|
|
|
Second Event
|
A1
|
A2
|
A3
|
Total
|
|
B1
|
2
|
2
|
3
|
7
|
|
B2
|
4
|
4
|
2
|
10
|
|
|
|
|
|
|
|
Total
|
6
|
6
|
5
|
17
|
|
|
|
|
|
|
| |
(a) Determine P(A3). (Round your answer to 2 decimal places.)
(b) Determine P(B2|A2). (Round your answer to 2 decimal places.)
(c) Determine P(B1 and A2). (Round your answer to 2 decimal places.)
3. All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .80, the probability the second truck is available is .55, and the probability that both trucks are available is .40:
What is the probability neither truck is available? (Round your answer to 2 decimal places.)
4. The credit department of Lion's Department Store in Anaheim, California, reported that 22 percent of their sales are cash or check, 24 percent are paid with a credit card and 54 percent with a debit card. Twenty percent of the cash or check purchases, 80 percent of the credit card purchases, and 65 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.)
5. Solve the following:
(a) 50!/46!
(b) 10P6 =
(c) 8C5 =
6. In a binomial distribution, and. Find the probabilities of the following events. (Round your answers to 4 decimal places.)
(a) Probability
(b) Probability
(c) Probability
7. In a Poisson distribution, . (Round your answers to 4 decimal places.)
(a) What is the probability that ?
Probability
(b) What is the probability that ?
Probability
8. Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top ten vehicles in terms of fuel economy.
(a) Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top ten. (Round your answers to 3 decimal places.)
(b) What is the likelihood that in the sample of three at least one Honda is included? (Round your answer to 3 decimal places.)
9. The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 224 customers on the number of hours cars are parked and the amount they are charged.
|
Number of Hours
|
Frequency
|
Amount Charged
|
|
1
|
|
16
|
|
$
|
3
|
|
|
2
|
|
33
|
|
|
8
|
|
|
3
|
|
43
|
|
|
12
|
|
|
4
|
|
43
|
|
|
15
|
|
|
5
|
|
37
|
|
|
22
|
|
|
6
|
|
16
|
|
|
24
|
|
|
7
|
|
6
|
|
|
27
|
|
|
8
|
|
30
|
|
|
30
|
|
|
|
|
|
|
|
|
|
|
|
|
224
|
|
|
|
|
|
|
|
|
|
|
|
|
| |
(a) Convert the data on frequency into a distribution of probabilities. (Round your answers to 3 decimal places.)
|
Hours
|
Probability
|
|
1
|
|
|
2
|
|
|
3
|
|
|
4
|
|
|
5
|
|
|
6
|
|
|
7
|
|
|
8
|
|
| |
(b-1) Find the mean and the standard deviation of the number of hours parked. (Round your intermediate values and final answers to 3 decimal places.)
(b-2) How long is a typical customer parked? (Round your answer to 3 decimal places.)
The typical customer is parked for hours
(c) Find the mean and the standard deviation of the amount charged. (Round your intermediate values andfinal answers to 3 decimal places.)
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 1, 2, 4, 6, 8, or 11 days last month.
|
Number of days absent
|
Probability
|
|
1
|
0.42
|
|
2
|
0.30
|
|
4
|
0.14
|
|
6
|
0.07
|
|
8
|
0.07
|
|
11
|
0
|
What is the variance of the number of days absent?
3.31
4.31
2.15
8.61