A package delivery service claims that no more than 5 percent of all packages arrive at the address late. Assuming that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected, and the 5 percent rate holds, what is the probability that exactly 2 packages in the sample arrive late?
A) 0.0746
B) 0.9884
C) 0.2347
D) 0.0439

Question

Quizplus · Accepted Answer

The probability of exactly 2 packages arriving late out of 10, given a 5% late arrival rate, can be calculated using the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=10$, $k=2$, $p=0.05$. Plugging these values in gives $P(X=2) = \binom{10}{2}(0.05)^2(0.95)^8 = 0.0746$.

A Package Delivery Service Claims That No More Than 5