8. Describe the two conditions that must be satisfied for random sampling. (1-point each) 9. The diameters of the trees in a stand of 100-year-old Ponderosa Pines are normally distributed with a mean of 15 inches and a standard deviation of 4 inches. If only trees with diameters of 10 inches or more are marketable, what proportion of the stand is marketable. (2-points) 10. GRE scores for seniors taking the psychology test are approximately normally distributed with a mean of 463 and a standard deviation of 75. a. What proportion of the population would have scores between 450 and 650? (3-points) b. What proportion would have scores above 720? (2-points) c. If 20,000 psychology majors took the test, how many would be expected to have scores above 670 (the highest score yet made by a recent State U. graduate)? (2-points) d. Find the raw scores that separate the middle 95 percent of the distribution from the lower 2 1/2 percent and the upper 2 1/2 percent. (3-points) e. The lowest score that gets a passing grade from the State U. Psychology Department on their comprehensive examination is 440. What proportion majors would be expected to pass? (2-points) 1 1. According to Obi-Wan Kenobi, the last of the Jedi Knights, "The Force can have an influence on the weak-minded." Please answer the following question which you will have no difficulty with; which you will answer quickly, completely, and correctly. The beautiful Princess Leia, in a prescience trance, saw a funny hair style on 1920s movie stars in America. She decided to adopt this hair style and practiced and practiced winding her hair in circles using her ears as cores. On the average she got 12 coils and the standard deviation was two coils. What is the probability that, on the day she was rescued by Luke, Han, and Chewbacca, she had between 12 and 15 coils? (3-points)