4. A probability density function is a function, ffx} , for which the probability that another quantity; X . is between a and b is equal to the area under y =f{_t'] for a 5x5 b. In statistics, X is called a continuous random variable, and the notation Pl}: 5 X Eb] is used for "the probability that X is between the values a and b ." 5o, PlaEX Sb}=area under _}"=fl:_f} for HEIEb. The Normal (or, Gaussianl distribution occurs frequently in nature; its density function is the famous I"bell curve,\" I 4.15:3 fir} =59 Forcing the mean to be ,u = [I and standard deviation to be 0' = 1 produces the Standard Normal [related to 1: , which can be shifted by the mean ,u' and compressedfexpanded by a standard deviation 0'. scores] which has the following graph. The Standard Normal can be constructed from any other Normal distribution. The very thin left and right side means that a normally-distributed variable, X , will be within 1, 2 ,or 3 standard deviation of the mean [over or under} with probability approximately {53.27% , 95.45 \"fa, and 99.?3 'l'u, respectively. {A} Estimate Pm E X E l} by shading a region on the graph above and approximating its area using any Riemann sum with 5 rectangles, labeled appropriately as 35,115 or M, . Round your answer to three decimal placesJ one decimal place when expressed as a percent. [opts] Use the function f on the previous page to compute the requested Riemann Sums approximationg each probability for the Standard Normal Distribution. Write each Riemann Sum in sigma notation before evaluating with technology and rounding to three decimal places, one decimal place when expressed as a percent. Show your work for Ax , label it, and label your final answer. (B) Estimate P(0 S x 1) by calculating Ro and R,00 . (10pts) (C) Estimate P(-1 S.x $1) using a right-hand Riemann Sum with / = 200. (5pts) (D) Estimate P(-2 S x 52) using a midpoint Riemann Sum with n = 40. (6pts) (E) Estimate P(-3 S x