It is known that screws produced by a certain company will b defective with probability .01 independently of each other. the company sells the screws in packages of 25 and offers a money back guarantee that at most 1 of the 25 is defective, using poisson approximation for binomial distribution the probability that the company must replace a package is approximatelya).01b).1947c).7788d). 0264e).2211

d).0264

Step-by-step explanation:

Given : It is known that screws produced by a certain company will b defective with probability .01 independently of each other.

The company sells the screws in packages of 25 and offers a money back guarantee that at most 1 of the 25 is defective.

Let x be the binomial variable that represents the defective screws having parameter p= 0.01 and n= 25

For using Poisson approximation for binomial distribution

Mean  =

Poisson distribution formula :

Now, the probability that the company must replace a package is

=Probability that package has more than 1 defectives

=

Hence, the required probability is 0.0264

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