1. A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data appear to confirm the belief that one design is just as likely to be selected as another? Explain.
|
Design
|
Number of Times Preferred
|
|
1
|
5
|
|
2
|
15
|
|
3
|
30
|
|
4
|
40
|
|
5
|
10
|
2. The U.S. adult population by age is as follows (The World Almanac, 2009). The data are in millions of people.
|
Age
|
Number
|
|
18 to 24
|
29.8
|
|
25 to 34
|
40.0
|
|
35 to 44
|
43.4
|
|
45 to 54
|
43.9
|
|
55 to 64
|
32.7
|
|
65 and over
|
37.8
|
Assume a person will be randomly chosen from this population.
a. What is the probability the person is 18 to 24 years old?
b. What is the probability the person is 18 to 34 years old?
c. What is the probability the person is 45 years or older?
3. Assume that we have two events.A and B. that are mutually exclusive. Assume further that we know P(A) =.30 and P(B) =.40
a. What is P(A ∩ B)?
b. What is P(A | B)?
c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same , and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.
d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?