Problem 6. An FBI survey shows that about 30% (i.e., 0.3) of all property crimes go solved. Suppose that in New York City 15 such crimes are committed and they are each deemed independent of each other. Hint use binomial distribution formula given on Page number 203. a) What is the probability that exactly 3 of these 15 crimes will be solved? ( 2 points) Hint use binomial distribution formula b) What is the probability that at most 3 of these 15 crimes will be solved? (2 points) Hint use binomial distribution formula P (at most 3 successes) = P(x 3 3) = P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3) c) What is the probability that more than 11 of these 15 crimes will be solved? (2 points) Hint use binomial distribution formula P (more than 11 crimes will be solved successes) = P(x > 11) = P(x >12) + P(x > 13 )+ P(x > 14)+ P(x > 15) Problem 5. Given the number of trials and the probability of success, determine the probability indicated: Hint use binomial distribution formula a. n = 15, p = 0.4, find P(4 successes) ( 1 points) b. n = 12, p= 0.2, find P(2 success ) ( 1 points) c. n= 20, p = 0.05, find P(at most 3 successes) (2 points) (hint for c. P (at most 3 successes) = P(x