Math 150 - CW#15: Normal Distributions Clearly and neatly show all work for each problem. 1. Project Scores Professor Heidt has decided to take a closer look at the grades on the consumer math projects from his Survey of Math courses. Assuming that class averages are normally distributed with a mean of 75 and a standard deviation of 15 (a highly unlikely assumption), find the percentage of scores that fall into the following ranges: (Do NOT round your answers) a) Less than 90 b) Less than 65 c) More than 70 d) More than 82 e) Between 60 and 90 f) Between 72.5 and 89.4 2. Curving the Course Finally, Professor Heidt has determined that the scores from his Survey of Math class were normally distributed. After finding the mean and standard deviation of the scores, he has decided to assign letter grades using the following breakdown. . And any student with a z-score below a -1.8 will get an F. . Any student with a z-score between -1.8 and -1.2 will get a D. . Any student with a z-score between -1.2 and 0.6 will get a C. . Any student with a z-score between 0.6 and 1.5 will get a B. . Any student with a z-score higher than 1.5 will get an A for the course. If Professor Heidt has 30 students in his class, how many students will get an A, B, C, D, and F? Round your final answers to the nearest whole student. (Note: You do NOT need to calculate z-scores. The z-scores are provided to you.) MTH 150 - Heidt Help Allowed