Poissson distribution In order to control the polishing quality of a lens, a certain company is...

Poissson distribution

In order to control the polishing quality of a lens, a certain company is used to finish the number of spots on the surface considering the defective lens if 3 or more spots appear on it. The average rate is 2 defects per cm2. Calculate the probability that a 4cm2 lens will not be classified as defective.

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Expert Solution

Solution:

we are given that: In order to control the polishing quality of a lens, a certain company is used to finish the number of spots on the surface considering the defective lens if 3 or more spots appear on it.

So if there are 2 or fewer spots , then it is not classified as defective.

We have the average rate is 2 defects per cm2, then average rate of defective per 4 cm2 lens will be 2 * 4 = 8 defects per 4 cm2. That is:

We have to find:

P( 4 cm2 lens will not be classified as defective)=.............?

That is:

P( number of defects are less than or equal to 2 ) = ..........?

Using Poisson probability distribution:

Use excel or scientific calculator to find e^-8 = 0.0003355

Thus the probability that a 4cm2 lens will not be classified as defective is 0.013754

milcah answered 5 months ago

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