[7](12) Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its prob- ability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12, 429 children. a) Assuming that neuroblastoma occurs as usual, what distribution do you apply to this situation? Explain. b) Using the distribution you describe in (a), find the mean and standard deviation of cases in groups of 12, 429 children. c) Find the probability that the number of neuroblastoma cases in a groups of 12, 429 children is 0 or 1. d) Does the cluster of four cases in Oak Park, Illinois, appear to be attributable to random chance? Why or why not? [8](9) Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112 (based on data from the College Board). Randomly selected men are given the Columbia Review course before taking the SAT test. Assume that the review course has no effect. a) If 16 of the men are randomly selected, find the probability that their mean score is at least 590. b) In finding the probability for part (b), why can the Central Limit Theorem be used even though the sample size doesn't exceed 30? Explain. cj If the random sample of 16 men does result in a mean score of 590, is there strong evidence to support the claim that the course actually effective? Explain why or why not