Suppose that a random variable is normally distributed with mean = 2 and variance o = 16 (we write X~ N(2, 16)). We will calculate the probability that the random variable takes on a value less than or equal to 0 (P(X 0)) in several steps. a. First, write down the mathematical expression for finding P(X 0) in terms of the PDF f(x). You do not need to substitute in the formula for the PDF f(x) of a normal distribution or solve the integral. Just write the expression. b. Sketch a plot of the PDF of this random variable. Be sure to label the mean and standard deviation. On your plot, also shade the area that tells us P(X 0). c. In part a, you should have written down a very generic formula for P(X < 0) involving an integral and the PDF f(x). This would be complicated to solve, so lets use the standardized normal distribution instead. First, write down the z-score for the value 0. d. Now, instead of finding P(X 0), we would like to find P(Z zo), where Z = X-" and zo is the z-score you found in part c. Use the standard normal probability table on Canvas and find P(Z zo).