(iii) 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 (i) = f(x) 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X (ii) 0.008 f(x) 0.007- 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X 375, and m = 250 on the x-axis. Choose the correct graph below. (iii) 0.008 f(x) 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X (iv) 0.008 0.007 Graph (i) f(x) 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X

(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.

(b) What is the probability that the random variable will assume a value between 100 and 250? If required, round your answer to four decimal places.

(c) What is the probability that the random variable will assume a value greater than 320? If required, round your answer to four decimal places.