13) [9 marks] Standard Normal Distribution. g Let f(z) = '/12=eT. This function plays a fundamental role in probability theory and statistics. The graph of this function is the famous \"bell curve\" and the function is called the probability density function for the standard normal distribution. has 5 2 - i e a) One very important fact about this function is that the area under the graph is exactly 1. As evidence of this, use Maple to calculate the upper and lower Riemann sums for the n- regular partition over the interval [0,25] using n=10000. i) U(f, Pioooo) =7 ii) L(f, Pioooo) =7 b) Use Maple to estimate f_ll \\/%e > dz. (In statistical terms this is the proportion of the data that lies within one standard deviation of the mean). i) J2, e dz =~ 0.6827. 2 i) [0, Ame? dz = 0.6715. iii) J7, e dz ~0.3413