Bottomline Ink, a forms managementcompany, fills 100 orders a day with a 2% error rate in the completed orders. Assume this to be a binomial distribution. What is the probability that there will be more than 5 order errors in a given day?
A) 0.0062
B) 0.4838
C) 0.9838
D) 2.1428

Question

Quizplus · Accepted Answer

We need to find the probability of more than 5 order errors in a day given the error rate of 2%. Since this is a binomial distribution problem, we can use the formula for cumulative probability: P(X > 5) = 1 - P(X <= 5) To find P(X <= 5), we can use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k) where n is the total number of orders (100), p is the probability of error (0.02), and k is the number of errors (0 to 5). So, P(X <= 5) = sum of [ (100 choose k) * 0.02^k * 0.98^(100-k) ] for k = 0 to 5 This can be calculated using a calculator or spreadsheet, and the result is approximately 0.9938. Therefore, P(X > 5) = 1 - P(X <= 5) = 1 - 0.9938 = 0.0062. Thus, the answer is A.

Bottomline Ink, a Forms Managementcompany, Fills 100 Orders a Day