Homework SourseIn a survey conducted to see how long Americans keep their c
In a survey conducted to see how long Americans keep their cars, 2000 automobile owners were asked how long they plan to keep their present cars. The results of the survey follow. Find the probability distribution associated with these data. (Enter your answers to four decimal places.)
What is the probability that an automobile owner selected at random from those surveyed plans to keep his or her present car:
| Years Car Is Kept, x | Respondents | Probability |
|---|---|---|
| 0 ? x < 1 | 60 | |
| 1 ? x < 3 | 450 | |
| 3 ? x < 5 | 335 | |
| 5 ? x < 7 | 335 | |
| 7 ? x < 10 | 240 | |
| 10 ? x | 580 |
(a) Less than five years?
(b) 3 years or more?
(b) 3 years or more?
In a survey conducted to see how long Americans keep their cars, 2000 automobile owners were asked how long they plan to keep their present cars. The results of the survey follow. Find the probability distribution associated with these data. (Enter your answers to four decimal places.)
What is the probability that an automobile owner selected at random from those surveyed plans to keep his or her present car:
| Years Car Is Kept, x | Respondents | Probability |
|---|---|---|
| 0 ? x < 1 | 60 | |
| 1 ? x < 3 | 450 | |
| 3 ? x < 5 | 335 | |
| 5 ? x < 7 | 335 | |
| 7 ? x < 10 | 240 | |
| 10 ? x | 580 |
(a) Less than five years?
(b) 3 years or more?
(b) 3 years or more?
| Years Car Is Kept, x | Respondents | Probability |
|---|---|---|
| 0 ? x < 1 | 60 | |
| 1 ? x < 3 | 450 | |
| 3 ? x < 5 | 335 | |
| 5 ? x < 7 | 335 | |
| 7 ? x < 10 | 240 | |
| 10 ? x | 580 |
(a) Less than five years?
(b) 3 years or more?
(b) 3 years or more?
| Years Car Is Kept, x | Respondents | Probability |
|---|---|---|
| 0 ? x < 1 | 60 | |
| 1 ? x < 3 | 450 | |
| 3 ? x < 5 | 335 | |
| 5 ? x < 7 | 335 | |
| 7 ? x < 10 | 240 | |
| 10 ? x | 580 |
Solution
P(0 <X<1) = 60/2000 = 0.03
P(1 <X<3) = 450/2000 = 0.225
P(3 <X<5) = 335/2000 = 0.1675
P(5<X<7) = 335/2000 = 0.1675
P(7<X<10) = 240/2000 = 0.12
P(X>10) = 580/2000 = 0.29
a)
P(X<5) = 0.1675 + 0.225 + 0.03 = 0.4225
b)
P(X>=3) = 1- P(X<3)
= 1 - 0.225 - 0.03
= 0.745
