The article ?"Should You Report That Fender-Bender?" (Consumer Reports, Sept. 2013: 15) ?reported that 7 in 10 auto accidents involve a single vehicle (the article recommended always reporting to the insurance company an accident involving multiple vehicles). Suppose 15 accidents are randomly selected. Use Appendix Table A.1 to answer each of the following questions. a. What is the probability that at most 4 involve a single vehicle? b. What is the probability that exactly 4 involve a single vehicle? c. What is the probability that exactly 6 involve multiple vehicles? d. What is the probability that between 2 and 4, inclusive, involve a single vehicle? e. What is the probability that at least 2 involve a single vehicle? f. What is the probability that exactly 4 involve a single vehicle and the other 11 involve multiple vehicles?

Answer: Step 1 of 3 a. Here, p = 7/10 p = 0.7 n = 15 Now, the probability that at most 4 involve a single vehicle is P(X 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) Using Excel function “=BINOMDIST(x,n,p,false)” x P(x) 0 0.0000000143 1 0.000000502 2 0.00000820 3 0.0000829 4 0.000580575 Sum 0.00067222 Therefore, P(X 4) = 0.00067 0.001. b. Now, we need to find the probability that exactly 4 involve a single vehicle P(X = 4) = 0.000580575 0.001 Therefore, the probability that exactly 4 involve a single vehicle is 0.001. Step 2 of 3 6 15 6 c. Here, P(X = 6) = 15C 60.7) (1 0.7) = 5005 × 0.1176 × 0.000019683 = 0.01169 Therefore, the probability that exactly 6 involve multiple vehicles is 0.01169. d. Now, P(2 X 4) = P(X = 2) + P(X = 3) + P(X = 4) = 0.00000820 + 0.0000829 + 0.000580575 = 0.00067 0.001 Therefore, the probability that between 2 and 4, inclusive, involve a single vehicle is 0.001.