A hospital receives 625 of its flu vaccine vials from compan

A hospital receives 62.5% of its flu vaccine vials from company X and the remainder from other companies. Each shipment contains a very large number of vaccine vials. For Company X\'s shipments, 20% of the vaccine vials are defective. For the other companies, 8% of the vials are defective. The hospitals tests 5 randomly selected vials from a particular shipment. Calculate the probability that exactly 2 are defective.

Solution

To obtain 2 defective from a sample of 5, the parameter of Binomial distribution are,

For Company X,

sample size, n = 5,              Number of success, x = 2, Probability of success, p = 0.20                           

For Company Y,

sample size, n = 5,              Number of success, x = 2, Probability of success, p = 0.08

The Binomial probability can be obtained using Excel function BINOMDIST (x, n, p, 0).

Therefore, the Binomial probabilities will be,

For Company X,

BINOMDIST (2, 5, 0.20, 0) = 0.2048

For Company Y,

BINOMDIST (2, 5, 0.08, 0) = 0.0498

Since both the probabilities are independent of each other therefore, the required probability will be,

= (0.2048) (0.0498)

= 0.0102