The probability that an Oxnard University student is carrying a backpack is .70. If 10 students are observed at random, what is the probability that fewer than 7 will be carrying backpacks?
A).3504
B).2001
C).6177
D).2668

Question

Quizplus · Accepted Answer

The probability of fewer than 7 students carrying backpacks is the sum of the probabilities of 0, 1, 2, 3, 4, 5, or 6 students carrying backpacks. Using the binomial distribution, we can calculate these probabilities as follows:P(0 students carrying backpacks) = (10 choose 0) * (0.7)^0 * (0.3)^10 = 0.059049P(1 student carrying a backpack) = (10 choose 1) * (0.7)^1 * (0.3)^9 = 0.205891P(2 students carrying backpacks) = (10 choose 2) * (0.7)^2 * (0.3)^8 = 0.294630P(3 students carrying backpacks) = (10 choose 3) * (0.7)^3 * (0.3)^7 = 0.266806P(4 students carrying backpacks) = (10 choose 4) * (0.7)^4 * (0.3)^6 = 0.160084P(5 students carrying backpacks) = (10 choose 5) * (0.7)^5 * (0.3)^5 = 0.075630P(6 students carrying backpacks) = (10 choose 6) * (0.7)^6 * (0.3)^4 = 0.028452Therefore, the probability of fewer than 7 students carrying backpacks is:P(0 students carrying backpacks) + P(1 student carrying a backpack) + P(2 students carrying backpacks) + P(3 students carrying backpacks) + P(4 students carrying backpacks) + P(5 students carrying backpacks) + P(6 students carrying backpacks) = 0.059049 + 0.205891 + 0.294630 + 0.266806 + 0.160084 + 0.075630 + 0.028452 = 0.3504

The Probability That an Oxnard University Student Is Carrying a Backpack