A technician works on the mailing machines of companies in the Phoenix, Arizona area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same time frequency.
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Write My Essay For Me| x | f(x) |
| 1 | |
| 2 | |
| 3 | |
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| Total | 1.00 |
- Develop a probability distribution for a duration of a service call.
- Draw a graph of the probability distribution.
- Show that your probability distribution satisfied the two conditions required for a discrete probability function.
- What is the probability a service call will take three hours?
- The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.
| Payment ($)
x
|
Probability
f(x)
|
Xf(x)
|
| 0 | .85 | |
| 500 | .04 | |
| 1000 | .04 | |
| 3000 | .03 | |
| 5000 | .02 | |
| 8000 | .01 | |
| 10000 | .01 | |
| E(x) =μ = Σxf(x) =
|
- Use the expected value of collision payment to determine the collision insurance premium that would enable the company to break even.
- The insurance company charges an annual rate of $250 for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint: The expected payments from the company minus the cost of coverage.) Why does the policyholder decide to purchase a collision policy with this expected value?
- This following probability distributions of job satisfaction scores for a survey sample of information systems (IS) senior executives and (IS) middle managers range from 1 (very dissatisfied) to 5 (very satisfied).
| Job Satisfaction Score
(x) |
IS Senior Executives
f(x) – probability |
x f (x)
|
IS Middle Managers
f(x) – probability |
x f (x) |
| 1 | .05 | .04 | ||
| 2 | .09 | .10 | ||
| 3 | .03 | .12 | ||
| 4 | .42 | .46 | ||
| 5 | .41 | .28 | ||
| Sx f (x)= | Sx f (x)= |
- What is the expected value of the job satisfaction score for senior executives? ___
- What is the expected value of the job satisfaction score for middle managers? ___
| Job Satisfaction Score
(x) |
(x – μ)
Subtract the expected value of executives |
(x – μ)²
Square the value |
f(x)
|
(x – μ)²f(x)
|
| 1 | .05 | |||
| 2 | .09 | |||
| 3 | .03 | |||
| 4 | .42 | |||
| 5 | .41 | |||
| σ² =
|
- Compute the variance of job satisfaction scores for executives. _____
- Compute the standard deviation of job satisfaction scores for executives. _____
| Job Satisfaction Score
(x) |
(x – μ)
Subtract the expected value of middle managers |
(x – μ)²
Square the value |
f(x)
|
(x – μ)²f(x)
|
| 1 | .04 | |||
| 2 | .10 | |||
| 3 | .12 | |||
| 4 | .46 | |||
| 5 | .28 | |||
| σ² =
|
- Compute the variance of job satisfaction scores for middle managers. _____
- Compute the standard deviation of job satisfaction for the middle managers. _____
- Compare the overall job satisfaction of senior executives and middle managers given your interpretations of your findings.
- Delta Airlines quotes a flight time of 2 hours for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.
- Describe or show the graph of the probability density function, f(x), for a flight time in interval minutes (e.g., 100, 110, 120, etc.). You may use Excel or a similar software to obtain this image.
Example: What is the probability that the flight will be no more than 4 minutes late?
P(x £ 124) = Height (1/b-a)X Width (b-a) = (1/20) (124 – 120) = 0.20
- What is the probability that the flight will be no more than 5 minutes?
P(x < __) = Height (1/b-a)X Width (b-a) =
- What is the probability that the flight will be no more than 10 minutes late?
P(x < __) = Height (1/b-a)X Width (b-a) =
- What is the expected value flight time?
- What is the variance?
- What is the standard deviation?
- A sample of 50 Fortune 500 companies (Fortune, April 14, 2003) showed 5 were based in New York, 6 in California, 2 in Minnesota, and 1 in Wisconsin.
- Develop a sample estimate of the proportion of Fortune 500 companies based in New York.
- Develop a sample estimate of the number of Fortune 500 companies based in Minnesota.
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