Question

You have joined a military supplier building Trident nuclear submarines. You are to engineer the painting process. The painting process generates 3 defects per 100,000 square feet of submarine painted. The submarine has 75,000 square feet of surface area to be painted.

1-This is area. What distribution will you use to analyze number of defects?

2-What is the expected value (m) for the number of defects on one submarine?

3-What is the probability that you will have no defects on a painted submarine?

4-What is the probability that you will have one or more defects on a painted submarine?

5-What is the probability that you will have more than 3 defects?

Answer 1

Given that the painting process produces 3 defects per 100000sq ft. Then in 75000 sq ft, it will produce

defects.

1.

As the rate of occurance is very small while the area of occurence is very large, this can be well modelled by Poisson distribution with . Moreover number of defects is a discrete data. Let X be the number of defects on the submarine. Then,

2.

The expected value for the number of defects in one submarine is given by the mean of the distribution i.e. .

Thus the expected value for the number of defects is approximately 2.(Number of defects needs to be a whole number and thus the approximation is made.)

3.

Here we are to find P(X=0)

4.

Here we are to find

5.

Here we are to find

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