SOLUTION: THE MEAN NUMBER OF DEFECTIVE PRODUCTS PRODUCED IN A FACTORY IN ONE DAY IS 21.WHAT IS THE PROBABILITY THAT IN A SPAN OF 3 DAYS THERE WILL BE MORE THAN 58 BUT LESS THAN 64 DEFECTIVE

Algebra ->  Probability-and-statistics -> SOLUTION: THE MEAN NUMBER OF DEFECTIVE PRODUCTS PRODUCED IN A FACTORY IN ONE DAY IS 21.WHAT IS THE PROBABILITY THAT IN A SPAN OF 3 DAYS THERE WILL BE MORE THAN 58 BUT LESS THAN 64 DEFECTIVE       Log On


   

Question 1022899: THE MEAN NUMBER OF DEFECTIVE PRODUCTS PRODUCED IN A FACTORY IN ONE DAY IS 21.WHAT IS THE PROBABILITY THAT IN A SPAN OF 3 DAYS THERE WILL BE MORE THAN 58 BUT LESS THAN 64 DEFECTIVE PRODUCTS
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Question:
THE MEAN NUMBER OF DEFECTIVE PRODUCTS PRODUCED IN A FACTORY IN ONE DAY IS 21.WHAT IS THE PROBABILITY THAT IN A SPAN OF 3 DAYS THERE WILL BE MORE THAN 58 BUT LESS THAN 64 DEFECTIVE PRODUCTS

Solution:
Assuming the number of defective products of each day is independent of previous days, the Poisson distribution may be used to model this situation.
Average number of defects in 3 days = 3*21=63=λ.
P(k;λ)=λ^k*e^(-λ)/k!
We need to calculate
P(58 =0.04555+0.04783+0.04940+0.05020+0.05020
=0.2432