Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that no more than two calls are dropped.
A).9988
B).7613
C).8234
D).6736
E).4431

Question

Quizplus · Accepted Answer

The probability of no more than two calls being dropped can be calculated using the binomial probability formula, which is P(X = k) = (n choose k) * 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, and (n choose k) is the binomial coefficient. Here, n = 5 (since 5 calls are chosen), p = 0.05 (since there's a 5% chance of a call being dropped), and we're interested in the probability of k = 0, 1, or 2 calls being dropped.P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)Calculating each term:- P(X = 0) = (5 choose 0) * (0.05)^0 * (0.95)^5 = 1 * 1 * 0.95^5 ≈ 0.7738- P(X = 1) = (5 choose 1) * (0.05)^1 * (0.95)^4 = 5 * 0.05 * 0.95^4 ≈ 0.2036- P(X = 2) = (5 choose 2) * (0.05)^2 * (0.95)^3 = 10 * 0.05^2 * 0.95^3 ≈ 0.0216Adding these probabilities gives P(X ≤ 2) ≈ 0.7738 + 0.2036 + 0.0216 = 0.9990. The closest option to this calculated probability is A) .9988.

Five Percent of All International Video Calls on Interphone