Question

4. Imagine you are working with a local assembly plant and you are testing the parts coming off the line. You are looking for a particular defect for further testing, and so you must test all the parts until you find one with this particular defect. Assume the probability of any part having this defect is 0.03.

a. What is the expected number of parts you need to test until you find the first defective part?

b. What is the probability that you find a defective part on the very first part tested?

c. What is the probability that you find a defective part in the first 5 parts tested?

6. A forest has 17,000 acres. In general, a healthy forest has 80 trees per acre on average.

a. Assume the forest is a healthy forest. What is the expected number of trees in the forest?

b. Consider the ¼ acre immediately surrounding the point where the risen tree trail meets the fallen tree trail. What is the probability that this ¼ acre has less than 40 trees?

Answer 1

the random variable X, number of parts to be checked to get first defective part follows geometric distribution with probability, p=0.03.

a).

Mean of the geometric random variable is 1/p.

therefore, the expected number of parts to be checked until the first defective part obtained is 1/0.03 = 33.333.

b).

the probability that getting a defective part on the first trial is nothing but 0.03.

c).

the probability that getting a defective part in the first 5 parts tested is given below.

the required probability is 0.141266