Question

The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.5. What is the probability of observing exactly 2 errors in the carpet? round your answer to four decimal places.

Answer 1

Solution:

Given: The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.5.

That is: X = The number of weaving errors in a twenty-foot by ten-foot roll of carpet follows Poisson Distribution with parameter .

We have to find: the probability of observing exactly 2 errors in the carpet = ..........?

That is: P( X=2) = .........?

Poisson distribution:

Probability mass function of Poisson distribution is:

Use excel or scientific calculator to find: e^-0.5

e^-0.5 = 0.606531

Thus

Thus the probability of observing exactly 2 errors in the carpet is 0.0758