For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyzed. Find the probability that more than 79% of the sample Diamonds fail to qualify as gemstone grade.
A) 0.6879
B) 0.3121
C) 0.3594
D) 0.6406

Question

Quizplus · Accepted Answer

Let X be the number of diamonds that fail to qualify as gemstone grade in the sample. Then X follows a binomial distribution with n = 92 and p = 0.81.

We want to find P(X > 0.79*92) = P(X > 72.68). Since X is discrete, we need to use a continuity correction. That is, we need to find P(X > 73).

Using the binomial probability formula or a calculator, we get:

P(X > 73) = 1 - P(X ≤ 73) = 1 - binomcdf(92, 0.81, 73) ≈ 0.6879

Therefore, the best choice is A.

For a Particular Diamond Mine, 81% of the Diamonds Fail