Write a program in SAS Studio.

Suppose the collective weight of individuals on a busy elevator follows a normal distribution with a mean of 1000 pounds and a standard deviation of 150 pounds. a. Use the CDF() function in SAS to demonstrate the empirical rule for this situation. That is approximately 68% of the weights will be within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within 3 standard deviations. Print the three calculated probabilities to confirm the above. (Hint: Use SAS data lines consisting of three lines, each with two key input values for your CDF() functions). b. Demonstrate the symmetry of the normal distribution by showing the probability of having a weight greater than 1200 is the same as having a weight less than 800. Print the probabilities. c. Create a normal table of cumulative probabilities (probability of weight being less than the given value) for 11 values X = 500, 600, 700,..., 1300, 1400, 1500. Print the a resulting table such that no observation numbers appear and the probabilities column is labeled Probability < X. d. The maximum weight limit for the elevator is 1500 pounds. Only using the table you created in (c), do you feel the elevator is safe? Explain.