Consider the following to answer the question(s) below:
A courier service claims that no more than 5 % of all of its deliveries arrive late. Assuming deliveries are independent, a sample of 10 deliveries is randomly selected.
-What is the probability that more than 2 of the sample deliveries arrive late?
A) 0.0116
B) 0.0105
C) 0.0862
D) 0.0746
E) 0.0439

Question

Quizplus · Accepted Answer

The probability of a delivery arriving late is 0.05. The probability of a delivery arriving on time is 0.95. The probability of more than 2 deliveries arriving late is the complement of the probability of 0, 1, or 2 deliveries arriving late. The probability of 0 deliveries arriving late is 0.95^10 = 0.5987. The probability of 1 delivery arriving late is 10 * 0.05 * 0.95^9 = 0.2843. The probability of 2 deliveries arriving late is 45 * 0.05^2 * 0.95^8 = 0.1161. The probability of more than 2 deliveries arriving late is 1 - 0.5987 - 0.2843 - 0.1161 = 0.0009.

Consider the Following to Answer the Question(s) Below