A textile manufacturing process finds that on average, three flaws occur per every 220 yards of...

A textile manufacturing process finds that on average, three flaws occur per every 220 yards of material produced.

What is the probability of no more than two flaws in a 220-year piece of material? (Round your final answer to 4 decimal places.)

Expert Solution

Answer: 0.4232

Solution:

The event can be modeled as a poisson distribution.

where, poisson mean m = 3 ( 3 flaws per 220 yards)

Identity for poisson event is given by

Now we have to find the probability that no more than two flaws occur in a 220 yards, this can be found as follows

Also we could have used the cumulative poisson distribution table if provided, but this is a more general method to solve.

note -: since we are provided with the mean for 220 yards and also we have been asked to find the probability for the same 220 yards area, the means remain the same. and if we were asked let say for 110 yards we would have halved the number of flaws i.e 1.5 flaws per 110 yards, similarly if we were asked for 440 yards we would have doubled the mean value i.e 6 flaws per 440 yards.

orchestra answered 1 year ago

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