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 (Money, January 2009). Assume that the cost for this type of hospital emergency 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? (to 4 decimals) b.What is the probability that the cost will be less than $250? (to 4 decimals) c.What is the probability that the cost will be between $300 and $400? (to 4 decimals) 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

Explanation / Answer

X follows a normal distribution

X~N(328,92)

Now probability that the cost will be more than $500
=P(x>500)
=1-P(X<=500)
=1-P((x-328)/92<=(500-328)/92)
=1-P(z<=1.8695)
=1-?(z)
=1-0.96925 (from z score table)
=0.0307

probability that the cost will be less than $250

=P(X<250)
=P(z<=(250-328)/92)
=P(z<= -0.847)
=?(-0.847)
=1-?(0.847)
=1-0.80233
=0.1976



probability that the cost will be between $300 and $400?

P(300<400)-p(x="">300)
=P(z<0.782)-P(z>-0.3043)
=P(z<0.782)-(1-P(z<= -0.3043))
=0.7823

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