Question

I've gotten two different answers for this Statistics problem. Can you confirm the correct answer? Thanks!!

A shipment of 50,000 transistors arrives at a manufacturing plant. The quality control engineer at the plant obtains a sample of 500 resistors and will reject the entire shipment if 10 or more of the resistors are defective. Suppose that 4% of the resistors in the whole shipment are defective. What is the probability that the engineer accepts the shipment? Do you believe the acceptance policy of the engineer is sound?

Answer 1

The probability that a randomly selected resistor is defective = 0.04

Let X denotes the number of resistors that are defective in a random sample of 500 resistors.

X ~ Binomial(n = 500, p = 0.04)

The probability mass function of X is

Now,

The probability that the engineer accepts the shipment

Since the probability is quite small, so one should believe that  the acceptance policy of the engineer is not so sound.