Question 4: A hospital has two identical inpatient units with nursing requirements (which we call demand) D; and D;. Suppose D; and D> are normally distributed with mean y; = 9, y2 = 12 and standard deviations 07 = 3 and 0> = 4. The hospital determines staffing levels of the two units independently to achieve a critical ratio of 0.75 (ratio of , to , + Co)- 1. Calculate the staffing requirements, rounded to the next highest 0.25 shift, in these two units. (4 points) 2. Calculate the probability that a patient who needs to be placed in Unit 1 will be boarded. Repeat the calculations for Unit 2. (4 points) 3. Suppose the demand patterns in the two units are positively correlated with a cor- relation coefficient of = 0.2. If the hospital decides to pool bed capacity in the two units and hire an optimal number of nurses after pooling, what is the probability that a patient who needs to placed in either Unit 1 or Unit 2 is boarded? (4 points) !Note, this strategy requires nurses to be cross trained to provide care for patients in either unit. Page 2 4. Comment on the role of the correlation coefficient r. In particular, explain whether a higher value of r will lead to more or less staffing requirements, and why. What would happen if r were negative? Based on your arguments, which types of inpa- tient units are better suited for pooling bed capacity? (3 points)