10. IQ Some IQ tests are standardized to a Normal model, with a mean of 100 and a standard deviation of 15. a) Draw the model for these IQ scores. Clearly label it, show- ing what the 68-95-99.7 Rule predicts. b) In what interval would you expect the central 95% of IQ scores to be found? c) About what percent of people should have IQ scores above 115? d) About what percent of people should have IQ scores between 70 and 85? e) About what percent of people should have IQ scores above 130?12. Stats test Suppose your statistics professor reports test grades as z-scores, and you got a score of 2.20 on an exam. a) Write a sentence explaining what that means. b) Your friend got a z-score of -1. If the grades satisfy the Nearly Normal Condition, about what percent of the class scored lower than your friend?14. IQs revisited Based on the Normal model M( 100, 15) describing IQ scores, what percent of people's IQs would you expect to be a) over 80? b) under 90? c) between 112 and 132?39. Trees A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees pro- vide an accurate description of the whole forest and that a Normal model applies. a) Draw the Normal model for tree diameters. b) What size would you expect the central 95% of all trees to be? c) About what percent of the trees should be less than an inch in diameter? d) About what percent of the trees should be between 5.8 and 10.4 inches in diameter? e) About what percent of the trees should be over 15 inches in diameter