1. Suppose X - N(275, 16) a) Find the Pr(X>294) (2 points) b) Find the Pr(255sX=297) (2 points) c) Find the 17th percentile of X (2 points) 2. Suppose the following table summarizes the BMI for a population of 8 participants in a weight loss program: Participant BMI A 32.6 B 31.7 C 26.8 D 29.3 E 25.4 F 33.2 G 29.4 H 26.9 a) Calculate u and o. (2 points)| Note: You can use Microsoft Excel to do these calculations. Paste the Excel table showing the calculations here. b) BMI of 2 30 is considered obese. Assume that this population follows a normal distribution. What proportion of women is obese? (2 points) c) BMI between (25, 29.9) is considered overweight. What proportion of this population is overweight? (2 points) 3. The SAT and ACT are standardized tests for college admission in the United States. Both tests include components that measure reading comprehension. Suppose that SAT critical reading scores are Normally distributed with a mean of 510 and standard deviation of 115. In contrast, ACT reading scores are Normally distributed with a mean of 20.5 and standard deviation of 5. a) Sam takes the SAT reading test and scores 660. Dave takes the ACT test and scores 28. Who had the superior score, Sam or Dave? (4 points) (Hint: Standardize Dave's and Sam's scores and compare the probabilities.) b) How high must a student score to be in the top 10% of the ACT scores? (3 points) c) How high must a student score to be in the top 5% of the SAT scores? (3 points)