For a particular diamond mine, 75% of the diamonds fail to qualify as "gemstone grade". A random sample of 110 diamonds is analysed. Find the probability that less than 81% of the sample diamonds fail to qualify as gemstone grade
A)0.0735
B)0.9265
C)0.0548
D)0.9452

Question

Quizplus · Accepted Answer

The probability that less than 81% of the sample diamonds fail to qualify as gemstone grade can be found using the binomial or normal approximation to the binomial distribution. Given that 75% fail to qualify, we expect 75% of 110, or 82.5 diamonds, to fail on average. We are looking for the probability of getting fewer than 81% of 110, which is fewer than 89.1 diamonds failing. This is a problem that typically requires the use of statistical tables or software to solve accurately. The correct answer (B) 0.9265 suggests that there is a 92.65% chance that less than 81% of the diamonds in the sample fail to qualify as gemstone grade, indicating the use of a normal approximation to the binomial distribution and finding the cumulative probability up to the point of interest.

For a Particular Diamond Mine, 75% of the Diamonds Fail