Suzy and her staff have estimated average bed demand and the standard deviation

ID: 3040004 • Letter: S

Question

Suzy and her staff have estimated average bed demand and the standard deviation in bed demand based on the current year’s patient census data in each of the three wards. Histograms of bed demand show that bed demand per day can be modeled with a normal distribution. The present capacity (number of beds) of each ward appear in the table.Determine the proportion of days that demand for beds will exceed capacity for each of the three wards.

Capacity of beds:

Obstetrics=30

Surgery=20

Pediatrics =24

Average Bed Demand Standard WARD Per Day Deviation Obstetrics 24 6.1 Surgery 13 4.3 Pediatrics 19 4.7

Explanation / Answer

Answer:

Suzy and her staff have estimated average bed demand and the standard deviation in bed demand based on the current year’s patient census data in each of the three wards. Histograms of bed demand show that bed demand per day can be modeled with a normal distribution. The present capacity (number of beds) of each ward appear in the table. Determine the proportion of days that demand for beds will exceed capacity for each of the three wards.

Average Bed Demand

Standard

WARD

Per Day

Deviation

Obstetrics

6.1

Surgery

4.3

Pediatrics

4.7

Capacity of beds:

Obstetrics=30

Z value for 30, z =(30-24)/6.1 = 0.98

P( x >30) = P( z > 0.98)

=0.1635

Surgery=20

Z value for 20, z =(20-13)/4.3 =1.63

P( x >20) = P( z > 1.63)

=0.0516

Pediatrics =24

Z value for 24, z =(24-19)/4.7 =1.06

P( x >24) = P( z > 1.06)

=0.1446