Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% 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 10 decisions. Then X follows a binomial distribution with n=10 and p=0.1.

We want to find P(X<2) = P(X=0) + P(X=1). Using the binomial probability formula, we have:

P(X=0) = (10 choose 0) * 0.1^0 * 0.9^10 = 0.3487
P(X=1) = (10 choose 1) * 0.1^1 * 0.9^9 = 0.3874

Therefore, P(X<2) = P(X=0) + P(X=1) = 0.3487 + 0.3874 = 0.7361, which is approximately 0.736.

So the statement is true.

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