A company realizes that 5% of its pens are defective.In a package of 30 pens,is it likely that more than 6 are defective? Assume that pens in a package are independent of each other.
A)Yes.
B)No.6 is more than 10% of 30.
C)No.The pens in a package are dependent on each other.
D)No.The chance of getting a defective pen changes depending on the pens that have already been selected.
E)No.There are more than two possible outcomes.

Question

Quizplus · Accepted Answer

We can calculate the probability of having more than 6 defective pens using the binomial distribution. Let X be the number of defective pens in a package of 30 pens. Then X follows a binomial distribution with n = 30 and p = 0.05 (probability of defective pen). We want to find P(X > 6). Using a binomial calculator, we get P(X > 6) = 0.025, which is a low probability. Therefore, it is unlikely that more than 6 pens are defective in a package of 30 pens. The answer is (A).

A Company Realizes That 5% of Its Pens Are Defective