A random variable has a triangular probability density function with a = 50, b = 375, and m = 250. (a) Sketch the probability distribution function for this random variable. Label the points a = 50, b = 375, and m = 250 on the x-axis. Choose the correct graph below. (1) 0.008 0.007 0.006 0.005 fix 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 (ii) 0.008 0.007: 0.006 0.005 f(x) 0.004 0.003 0.002 0.001 + 0 0 50 100 150 200 400 250 300 350 400 (iii) 0.0081 0.007 0.006 0.005 (x)} 0.004 0.003 0.002 0.001 0 50 100 150 200 250 300 350 400 (iv) 0.0081 0.007 0.006 0.005 f(x) 0.004 0.003 0.002 0.001 0 0 50 100 150 400 200 250 300 350 400 X Graph (iv) (b) What is the probability that the random variable will assume a value between 60 and 250? If required, round your answer to four decimal places. 0.0046 (c) What is the probability that the random variable will assume a value greater than 280? If required, round your answer to four decimal places. 0.0865