8) Sweetwater & Associates (S&A) write weekend trip insurance at a nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0003. Suppose S&A wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed? (Hint: Find the mean and use Poisson)

Group of answer choices

0.8187

0.2500

0.0097

0.0243

9) A farmer who grows genetically engineered corn is experiencing trouble with corn borers. Many of the ears contained no borers. Some ears had one borer; A few had two borers, and so on. The distribution of the number of borers per ear approximated the Poisson distribution. Of the 5,000 ears counted 2,750 had at least one bore. What is the probability that an ear of corn selected at random will contain no borers?

Group of answer choices

0.5769

0.4966

1.000

0.0631

10) the mean a number of burglaries in a particular community is 2.9 per month. Let X refer to the number of burglaries that take place in a given month. Find the probability that five burglaries take place in this community in the coming month given that the requirements for the Poisson probability distribution are met.

Group of answer choices

0.1256

0.1260

0.1264

0.0940

11) Is the following experiment binomial? The percentage of sophomores at a certain liberal arts college is 29%. A random sample of 500 students from the college is taken and the number of sophomores in the sample is recorded.

Group of answer choices

Yes.

No, each trial has more than two possible outcomes.

No, the outcomes are not independent.

No, the probability of success is not constant.

12) A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 200 cars produced, there were 45 defective cars. Some of the cars had no defects, a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 200 cars produced, about how many out of every 1,000 cars assembled should have one or more defects?

Group of answer choices

About 660

About 165

About 200

About 330

13) For a binomial distribution, the mean is 4.0 and n = 10. What is p for this distribution?

Group of answer choices

0.6

1.00

4.0

0.4