Q No. 1: Raj Gandhi, supervisor of traffic signals for the Northern Division's State Highway Administration (SHA), must decide whether to install a traffic light at the reportedly danger- ous intersection of State Highway SH-4 and State Highway SH-7. Toward this end, Raj has collected data on accidents at the intersection: Number of Accidents Year J F M A MJ J A S O N D 1995 10 8 10 6 9 12 2 10 10 0 7 10 1996 12 9 7 8 4 3 7 14 8 8 4 SHA policy is to install a traffic light at an intersection at which the monthly expected number of accidents is higher than 7. According to this criterion, should Raj recommend that a traffic light be installed at this intersection?Q No. 6: Many samples of water, all the same size, are taken from a river sus- pected of having been polluted by irresponsible operators at a sewage treatment plant. The number of coiiform organisms in each sample was counted; the average number of organisms per sample was 15. Assuming the number of organisms to be Poisson distributed, nd the probability that: (a) The next sample will contain at least 20 organisms. (h) The next sample will contain no more than ve organisms. Q No. 4: Medical research has concluded that people experience a common cold roughly two times per year. Assume that the time between colds is nor- mally distributed with a mean of 160 days and a standard deviation of 40 days. (a) What is the probability of going 200 or more days between colds? Of going 365 or more days? (b) What is the probability of getting a cold within 80 days of a previous cold? Q No. 5: Assume that the test scores for a large class are normally distributed with a mean of 74 and a standard deviation of 10. (a) Suppose that you receive a score of 88. What percent of the class received scores higher than yours? (b) Suppose that the teacher wants to limit the number of A grades in the class to no more than 20%. What would be the lowest score for an A? QNO.3 A University found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a) Compute the probability that two or fewer will withdraw. b) Compute the probability that exactly four will withdraw. c) Compute the probability that more than three will withdraw. (1) Compute the expected number of withdrawals. e) Compute the variance and standard deviation of the number of withdraw