For a particular diamond mine, 78% of the diamonds fail to qualify as "gemstone grade". A random sample of 106 diamonds is analyzed. Find the mean $\underset { p } { \mu ^ { \wedge } }$
A) 0.96
B) 0.22
C) 0.040
D) 0.78

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is given by $\mu = np$, where $n$ is the number of trials (in this case, 106 diamonds) and $p$ is the probability of success (in this case, the probability of a diamond qualifying as gemstone grade, which is 1 - 0.78 = 0.22). However, the question seems to ask for the mean proportion ($\mu^\wedge$) of diamonds that fail to qualify, which directly corresponds to the given failure rate of 78% or 0.78, not requiring the calculation involving the sample size.

For a Particular Diamond Mine, 78% of the Diamonds Fail μ∧p\underset { p } { \mu ^ { \wedge } }pμ∧​

For a Particular Diamond Mine, 78% of the Diamonds Fail $\underset { p } { \mu ^ { \wedge } }$