Federal resources have been tentatively approved for the con

Federal resources have been tentatively approved for the construction of an outpatient clinic. In order to design a facility that will handle patient load requirements and stay within a limited budget, the designers studied patient demand. From studying a similar facility in the area, they found that the distribution of the number of patients requiring hospitalization during a week could be approximated by a normal distribution with a mean of 125 and a standard deviation of 27.

a. Use the Empirical Rule to describe the distribution of y, the number of patients requesting service in a week.
What interval should contain approximately 68% of the weeks? 125 ± ___________

What interval should contain approximately 95% of the weeks?
125 ± ___________

What interval should contain approximately 99.7% of the weeks?
125 ± ______________

b)  If the facility was built with a 180-patient capacity, what fraction of the weeks might the clinic be unable to handle the demand?   

Solution

68% population falls in Mean +- 1 x (Standard deviation)

95% population falls in Mean +- 2 x (Standard deviation)

99.7% population falls in Mean +- 3 x (Standard deviation)

Hence:

What interval should contain approximately 68% of the weeks?

125 ± 27

What interval should contain approximately 95% of the weeks?
125 ± 54

What interval should contain approximately 99.7% of the weeks?
125 ± 81

b)

We need a probability that X > 180

P (X > 180) = 1 - P(X<180)

= 1 - 0.9791

= 0.0209

i.e 2.09% of the times, the hospita will be unable to control the demand

Hope this helps.