It is known that screws produced by a certain company will be defective with a p

Question

It is known that screws produced by a certain company will be defective with a probability of .01 independently of each other. The company sells the screws in packages of 25 and guarantees that, at most, only one of the screws will be defective. If 2 or more screws are defective, the customer is entitled to his or her money back. Using Poisson approximation for binomial distribution, the probability that the company must replace a package is approximately____?
a) 0.01   b)0.1947   c)0.7788    d)0.0264    e)0.2211

Explanation / Answer

Solution:- d) The probability that the company must replace a package is 0.026.

p = 0.01

n = 25

x = 2

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 2) = 0.026

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