Suppose that a judge's decisions follow a binomial distribution and that his verdict is correct 90% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

Question

Quizplus · Accepted Answer

Let X be the number of incorrect verdicts in his next 10 decisions. Then X follows a binomial distribution with n=10 and p=0.1 (since he is correct 90% of the time, he is incorrect 10% of the time). We want to find P(X<2), which can be calculated using the binomial cumulative distribution function:

P(X<2) = P(X=0) + P(X=1) = bincdf(10,0.1,1) = 0.736

Therefore, the statement is true.

Suppose That a Judge's Decisions Follow a Binomial Distribution and That