The probability that an Oxnard University student is carrying a backpack is 0.70.If 10 students are observed at random,what is the probability that fewer than 7 will be carrying backpacks?
A)0.3504
B)0.2001
C)0.6177
D)0.2668

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. This can be calculated using the binomial distribution:P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)= (10 choose 0) * (0.70)^0 * (0.30)^10 + (10 choose 1) * (0.70)^1 * (0.30)^9 + (10 choose 2) * (0.70)^2 * (0.30)^8 + (10 choose 3) * (0.70)^3 * (0.30)^7 + (10 choose 4) * (0.70)^4 * (0.30)^6 + (10 choose 5) * (0.70)^5 * (0.30)^5 + (10 choose 6) * (0.70)^6 * (0.30)^4= 0.000001 + 0.000021 + 0.000147 + 0.000735 + 0.002704 + 0.007776 + 0.016533= 0.03504

The Probability That an Oxnard University Student Is Carrying a Backpack