For a particular diamond mine, 82% of the diamonds fail to qualify as "gemstone grade". A random sample of 102 diamonds is analyzed. Find the probability that less than 88% of the sample diamonds Fail to qualify as gemstone grade.
A) 0.0571
B) 0.9429
C) 0.0465
D) 0.9535

Question

Quizplus · Accepted Answer

The probability of a diamond failing to qualify as gemstone grade is 0.82. The probability of a diamond qualifying as gemstone grade is 1 - 0.82 = 0.18. The probability of less than 88% of the sample diamonds failing to qualify as gemstone grade is the probability of 0, 1, 2, ..., 17 diamonds failing to qualify as gemstone grade. This is given by the binomial distribution:P(X < 18) = ΣP(X = k) for k = 0, 1, 2, ..., 17= Σ(102 choose k) * (0.82)^k * (0.18)^(102-k) for k = 0, 1, 2, ..., 17= 0.9429Therefore, the probability that less than 88% of the sample diamonds fail to qualify as gemstone grade is 0.9429.

For a Particular Diamond Mine, 82% of the Diamonds Fail