a. Calculation:

The data represents the probability distributions of company's monthly demand for the past two years.

The formula for the expected value of a discrete random variable is,

\(\displaystyle{E}{\left({x}\right)}=\mu\)

\(\displaystyle=\sum{x}\cdot{f{{\left({x}\right)}}}\)

The expected monthly order quantity is obtained using the following table:

\begin{array}{|c|c|} \hline x&f(x)&x \cdot f(x) \\ \hline 300&0.20&60 \\ \hline 400&0.30&120\\ \hline 500&0.35&175\\ \hline 600&0.15&90\\ \hline Total&1.00&445\\ \hline \end{array}

Thus, the monthly order quantity should be 445 units.

The data represents the probability distributions of company's monthly demand for the past two years.

The formula for the expected value of a discrete random variable is,

\(\displaystyle{E}{\left({x}\right)}=\mu\)

\(\displaystyle=\sum{x}\cdot{f{{\left({x}\right)}}}\)

The expected monthly order quantity is obtained using the following table:

\begin{array}{|c|c|} \hline x&f(x)&x \cdot f(x) \\ \hline 300&0.20&60 \\ \hline 400&0.30&120\\ \hline 500&0.35&175\\ \hline 600&0.15&90\\ \hline Total&1.00&445\\ \hline \end{array}

Thus, the monthly order quantity should be 445 units.