Problem 3. Suppose Y~ N(90, 10). Find P(Y 84.8). Round your answer to four decimal places. Problem 5. Human height follows a normal distribution. In North America the average height for men is 5'9" (that's 69 inches) and the standard deviation is 2 inches. Find the interquartile range. Find the 90th percentile of the male height distribution. Round your answer to four decimal places. Problem 4. Suppose X is normally dis- tributed with mean = 45 and standard deviation o 10. Sketch the pdf of X. You don't have to label any points on the y-axis. Bonus problem: Let Z~ N(0, 1) and let Yunif(-3,3). Sketch the pdf's of Z and Y together on the same plot. Label the value of the y-intercept for each pdf.