Part I: Discrete Distributions

1. Suppose that airplane engines operate independently and fail with probability equal to 0.3. Assuming that a plane makes a safe flight if at least one-half of its engines run, determine whether a 4-engine plane or a 2-engine plane has the higher probability for a successful flight. Your solution must use one of the standard probability distributions to solve the problem.

2. A manufacturing process results in a part that is acceptable, needs rework, or fails in the ratio 8:3:2. Find the probability that among 100 parts, 61 will be acceptable, 24 will need rework, and 15 will fail.

3. Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at a rate of 8 per hour. Thus, the Poisson parameter for arrivals over a period of hours is µ= 8t.

- What is the probability that exactly 5 small aircraft arrive during a 1-hour period?
- What is the probability that at least 2 aircraft arrive during a 1-hour period?
- If we define a working day as 12 hours, what is the probability that at least 95 small aircraft arrive during a workday?

4. What is the probability that a waitress will refuse to serve alcoholic beverages to only 2 minors if she randomly checks the ID’s of 5 among 9 students, 4 of whom are minors?

5. A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 25 items are readied for shipment, and a sample of 3 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped.

- What is the probability that a box containing 2 defectives will be shipped?
- What is the probability that a box containing only 1 defective will be sent back for screening?

** by using Excel and formula**

**I need it Excel file**

**thanks**

Subject | Mathematics |

Due By (Pacific Time) | 11/29/2013 12:00 am |

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