4. ThefollowinglistoftestscoreshasanaverageofSOandanSDoflO: 39 41 47 58 65 37 37 49 56 59 62 36 48 52 64 29 44 47 49 52 53 54 72 50 50 (a) Usetheclassintervals20~30,30~40,40~50,50~60,60~70, 70~80todraw a histogram with the vertical scale being the density scale. Then on the same picture, convert the original scales (both horizontal and vertical) into the standard units, and sketch the normal curve on the picture. (10 points) (b) Use the normal approximation to estimate the number of scores within 1.25 SDs of the average. (5 points) (c) If one student claims his score is higher than 96% of his classmates, use the normal approximation to estimate his score. In reality, what is the 96th percentile of the scores distribution of the above list? (15 points)