In an article about the cost of health care, Money magazine reported that a visi

Question

In an article about the cost of health care, Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $328. Assume that the cost for this type of hospital emergence room visit is normally distributed with a standard deviation of $92. Answer the following questions about the cost of a hospital emergency room visit for this medical service. a. What is the probability that the cost will be more than $500? b. What is the probability that the cost will be less than $250? c. What is the probability that the cost will be between $300 and $400? d. If the cost to a patient is in the lower 8% of charges for this medical service, what was the cost of this patient's emergency room visit?

Explanation / Answer

Ans:

mean=328

standard deviation=92

a)

z=(500-328)/92=1.87

P(z>1.87)=0.0308

b)

z=(250-328)/92=-0.85

P(z<-0.85)=0.1977

c)

z(300)=(300-328)/92=-0.30

z(400)=(400-328)/92=0.78

P(-0.3<=z<=0.78)=P(z<=0.78)-P(z<=-0.30)=0.7823-0.3821=0.4002

d)

P(Z<=z)=0.08

z=-1.405

x=328-1.405*92=198.74

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