The manager of a certain toy company has decided to accept a shipment of electronic games if none of a random sample of 20 is found to be defective. What is the probability that he will accept the shipment if 15% of the electronic games is defective? What is the probability that he will accept the shipment if 8% of the electronic games is defective?

Question

The manager of a certain toy company has decided to accept a shipment of electronic games if none of a random sample of 20 is found to be defective. What is the probability  that he will accept the shipment if 15% of the electronic games is defective? What is the probability  that he will accept the shipment if 8% of the electronic games is defective? ​
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Quizplus · Accepted Answer

We can model the situation with a binomial distribution, where success is defined as receiving a non-defective electronic game.

For the first scenario, where 15% of the electronic games are defective, the probability of success (p) is 0.85. We need to find the probability that all 20 games in the sample are non-defective, which is:

P(X = 20) = (0.85)^20 = 0.0264

Therefore, the probability of accepting the shipment is 0.0264, or approximately 2.64%.

For the second scenario, where 8% of the electronic games are defective, the probability of success (p) is 0.92. Again, we need to find the probability that all 20 games in the sample are non-defective:

P(X = 20) = (0.92)^20 = 0.1626

Therefore, the probability of accepting the shipment is 0.1626, or approximately 16.26%.

Since the question asks for the probability of accepting the shipment under both scenarios, the best choice is B, which provides the probability of accepting the shipment for each scenario.

The Manager of a Certain Toy Company Has Decided to Accept