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Based on a Quinnipiac University poll, 39% of U

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Based on a Quinnipiac University poll, 39% of U.S. adults believe that the federal government has handled climate change properly. A random sample of 12 adults is taken from the population. Using a binomial probability model, what is the likelihood that between 3 and 7 people in the sample believe the government has handled climate change properly? (10 points) 6. The probability that a child develops neuroblastoma, a rare form of cancer, is 0.000011 (11 in 1 million). Assuming that neuroblastoma occurs as usual and using a Poisson probability model, does a cluster of 4 cases among a group of 12,429 children appear to be attributable to random chance? Briefly explain why or why not. (10 points) 7. Is the 60th percentile of any normal distribution always greater than the mean? Briefly explain why or why not. (10 points) 8. In a study of facial behavior (Pittman, Olk, Orr, and Singh), people in a control group are timed for eye contact in a 5-minute period. Their times are normally distributed with a mean of 184.0 seconds and a standard deviation of 55.0 seconds. Find the number of seconds r for which the probability that a randomly selected subject has eye contact time greater than or equal to x is 0.05. (10 points) 9. A model for pulse rates (beats per minute) for female adults assumes that pulse rates are normally distributed with a mean of 74.0 bpm and a standard deviation of 12.5 bpm. A random sample of 16 female adults is taken, and the sample mean of their pulse rates is found to be 70.2 bpm. Is this sample mean a significantly low value among the distribution of sample means? (10 points) 10. A study from Indiana University suggests that 12% of all people have green eyes. In a sample of 650 people, 86 of them have green eyes. Determine the normal distribution approximation to the binomial random variable of number of people with green eyes among the 650 subjects and give the corresponding z-score for x = 86. (10 points)