Answer question 1,2,3 based on material below.

1. The number of patients within each service line on any day is a random variable. Assume that this random variable has a normal distribution with the standard deviation equal to the square root of the mean. For example, for the head injury service line, the mean is 9.07 and the standard deviation is907 =3.01. According to Kramer's assumptions, each physical therapist can serve three patients Thus, three physical therapists in the head injury service line have the capacity to treat nine patients per day. Since the average number of patients is 9.07, with three physical therapists, the probability is about 0.5 that the demand for physical therapy will not be met. Suppose you assigned four physical therapists to the head injury line. What is the probability that the demand for physical therapy will not be met on a particular day? Suppose the management would like to have a service level of at least 95%. That is, the probability that the demand for physical therapy will not be met on any given day should be less than 5%. How many physical therapists would you assign to the head injury service line?

2 . How many physical therapists would you assign to each of the other four other service lines? What is the total number of physical therapists required under the service line organization? Compare that number to how many you would need if the physical therapists were organized in a single physical therapy department, as is currently the case, rather than in the proposed five service lines. Explain your results.

3. In what other ways could Kramer organize the physical therapists? What other options, if any, can you suggest to capture the benefits of the service lines while still maintaining a reasonable level of physical therapist utilization? Justify your suggestion.