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.

(i) \[ \begin{array}{c}
0.008 \\
0.007 \\
0.006 \\
0.005 \\
0.004 \\
0.003 \\
0.002 \\
0.001 \\
0 \\
50 \quad 100 \quad 150 \quad 200 \quad 250 \quad 300 \quad 350 \quad 400 \\
\end{array} \]

(ii) \[ \begin{array}{c}
0.008 \\
0.007 \\
0.006 \\
0.005 \\
0.004 \\
0.003 \\
0.002 \\
0.001 \\
0 \\
50 \quad 100 \quad 150 \quad 200 \quad 250 \quad 300 \quad 350 \quad 400 \\
\end{array} \]

(iii) \[ \begin{array}{c}
0.008 \\
0.007 \\
0.006 \\
0.005 \\
0.004 \\
0.003 \\
0.002 \\
0.001 \\
0 \\
50 \quad 100 \quad 150 \quad 200 \quad 250 \quad 300 \quad 350 \quad 400 \\
\end{array} \]

(iv) \[ \begin{array}{c}
0.008 \\
0.007 \\
0.006 \\
0.005 \\
0.004 \\
0.003 \\
0.002 \\
0.001 \\
0 \\
50 \quad 100 \quad 150 \quad 200 \quad 250 \quad 300 \quad 350 \quad 400 \\
\end{array} \]

Graph (iv) is the correct graph.

(b) What is the probability that the random variable will assume a value between 50 and 250? If required, round your answer to four decimal places.

\[
0.6154
\]

(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.

\[
0.0745
\]