Approximately 1% of all USPS package deliveries are lost.You select 10 package deliveries at random.Use the binomial probability function to compute the probability that no more than one package will be lost.
A).8753
B).9958
C).9044
D).8842
E).9562

Question

Quizplus · Accepted Answer

The probability that no more than one package will be lost can be calculated using the binomial probability formula, which is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and nCk is the binomial coefficient. Here, n = 10, p = 0.01 (since 1% of packages are lost), and we want to find the probability of k = 0 or k = 1.For k = 0 (no packages lost): P(X = 0) = (10C0) * (0.01)^0 * (0.99)^10 ≈ 0.9044For k = 1 (one package lost): P(X = 1) = (10C1) * (0.01)^1 * (0.99)^9 ≈ 0.0914Adding these probabilities gives the total probability of no more than one package being lost: 0.9044 + 0.0914 = 0.9958.

Approximately 1% of All USPS Package Deliveries Are Lost