certain screw making machine produce on average of 2 defective screw out of 100 and pack them in boxes of 500 find the probability that a box contain 15 defective screws
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Given certain screw making machine produce on average of 2 defective screw out of 100 and pack them in boxes of 500 find the probability that a box contain 15 defective screws
- Given out of 100 screws an average of 2 defective screws is produced by a certain screw making machine. So the probability will be 2/100 = 0.02
- So we have Poisson’s distribution that is events occurring in a given time period.
- Now n = 500 and p = 0.02
- Therefore mean = λ = np
- = 500 x 0.02
- = 10
- Now the probability that a box contains 15 defective screws is λ ^15 / 15! X e^- λ
- 10^15 / 15! X e^- 10
- = 10^15 / 1307674368000 x e^-10
- = 764.716373182 x 0.0000453999
- = 0.0347
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