Question

A manufacturer ships toasters in cartons of 10. In each? carton, they estimate a 20?% chance that one of the toasters will need to be sent back for minor repairs. In a batch of 5,000 ?toasters, what are the chances that fewer than 950 need to be? returned?

Answer 1

Let X be the number of toasters need to send back for minor repairs

The probabiity that a toaster will need to sent back for minor repairs is p = 0.20

X ~Binomial ( 5000, 0.20)

Since sample size is very large , we can use normal approximation to binomial distribution if the condition and is satisfied

Since both conditions are satisfied, we use normal approximation

= 0.5-0.4616= 0.0384

Answer: There are 3.84% chances  that fewer than 950 need to be? returned.