I have to compute this separately from the first part. I can\'t find anything on
ID: 3178498 • Letter: I
Question
I have to compute this separately from the first part. I can't find anything on how to solve this. My instructor implied that this is an invNorm calculation.
East Mercy Hospital equation
Histogram plots of bed usage show a remarkably close approximation to a normal distribution for each ward. Note that it is possible for a ward to exceed its capacity, but according to state guidelines, this should not occur more than 5% of the time. Megan is in the process of preparing a report to the administrator showing how many beds are to be added to each of the three wards.
The equation is for the part below.
Given the state guidelines and the demand for beds, how many beds should be available in each of the wards? Round accordingly.
East Mercy Medical Center is located in a rapidly growing area and is feeling capacity limitations. In particular, according to staff personnel, the obstetrics, adult medical surgical, and pediatric wards are “bursting at the seams.” East Mercy is considering an extensive expansion program, including expansion of the obstetric, adult medical surgical, and pediatric wards. The Board of Trustees has allocated $400,000 for new beds in these three wards. Megan Jacobs is recently hired as assistant administrator and is charged with determining how many beds current demand levels justify for each ward and how many beds to actually add, given the $400,000 cost constraint. Her staff computed statistics based on the current year’s patient census data in each of the three wards. Ward Mean No. Beds Used Per Day Standard Deviation Present Capacity Cost of Adding 1 Bed + Supplies Obstetrics 24 6.1 30 $20,000 Surgery 13 4.3 20 $26,000 Pediatrics 19 4.7 24 $15,500Histogram plots of bed usage show a remarkably close approximation to a normal distribution for each ward. Note that it is possible for a ward to exceed its capacity, but according to state guidelines, this should not occur more than 5% of the time. Megan is in the process of preparing a report to the administrator showing how many beds are to be added to each of the three wards.
The equation is for the part below.
Explanation / Answer
Answer:
From the given data:
Cost constraint = $400,000$
Let the number of beds to be added to each Obstetrics, Surgery and Pediatrics department be N1, N2 and N3
Cost of adding 1 bed + supplies to Obstetrics department = $20,000
Cost of adding 1 bed + supplies to Surgery department = $26,000
Cost of adding 1 bed + supplies to Pediatrics department = $15,500
As per the cost constraint: 20000*N1 + 26000*N2 + 15500*N3 $ 40,000
It is mentioned that the demand of bed (bed usage) for each ward follows a normal distribution:
For Obstetrics Department: P((x-mean)/sd) < 0.05 (5%)
P((x-24)/6.1) < 0.05, where x = 30 + N1
P(30+N1-24)/6.1 < 0.05 This corresponds to a Z value of 1.65 for one tailed test.
(6+N1)/6.1 > 1.65
N1 > 4.065 OR conservatively 5. That means the number of beds in Obstetrics department should increase a minimum by 5
Similarly for other departments:
For Surgery Department: P((x-mean)/sd) < 0.05 (5%)
P((x-13)/4.3) < 0.05, where x = 20 + N2
P(20+N2-13)/4.3 < 0.05 This corresponds to a Z value of 1.65 for one tailed test.
(7+N2)/4.3 > 1.65
N2 > 0.095 OR conservatively 1. That means the number of beds in Surgery department should increase a minimum by 1
For Pediatrics Department: P((x-mean)/sd) < 0.05 (5%)
P((x-19)/4.7) < 0.05, where x = 24 + N3
P(24+N3-19)/4.7 < 0.05 This corresponds to a Z value of 1.65 for one tailed test.
(5+N3)/4.7 > 1.65
N3 > 2.755 OR conservatively 3. That means the number of beds in Surgery department should increase a minimum by 3
Based on these numbers, minimum cost of expansion required:
= 20000*N1 + 26000*N2 + 15500*N3 = 20000*(5) + 26000*(1) + 15500*(3) = $172500 which is < $400,000