Problem 1: Commuter arrival. The number of arrivals per minute at a Springfield railway station located close to the central business district between 6:00 AM to 9:20 AM was recorded with the following results: Arrivals Frequency 0 12 33 45 UT A WNA 42 31 19 8 7 3 a. Compute the expected number of arrivals per minute. b. Compute the standard deviation. Problem 2: Computer Company Plant Expansion. The J. R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company's president must determine whether to make the expansion a medium- or large-scale project. Demand for the new product is uncertain, which for planning purposes may be low demand, medium demand, or high demand. The probability estimates for demand are .30, .60, and .10, respectively. Letting x and y indicate the annual profit in thousands of dollars, the firm's planners developed the following profit forecasts for the medium- and large-scale expansion projects. Medium-Scale Large-Scale Expansion Profit Expansion Profit X f(x) X f(x) Low 75 0.30 75 0.30 Demand Medium 150 0.60 200 0.60 High 325 0.10 300 0.10 a. Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expected profit? b. Compute the standard deviation for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of minimizing the risk or uncertainty