In an article about the cost of health care Money magazine r

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) 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? (to 2 decimals)

Solution

Mean ( u ) =328
Standard Deviation ( sd )=92
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 500) = (500-328)/92
= 172/92 = 1.8696
= P ( Z >1.87) From Standard Normal Table
= 0.0308
b)
P(X < 250) = (250-328)/92
= -78/92= -0.8478
= P ( Z <-0.8478) From Standard Normal Table
= 0.1983                  
c)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 300) = (300-328)/92
= -28/92 = -0.3043
= P ( Z <-0.3043) From Standard Normal Table
= 0.38043
P(X < 400) = (400-328)/92
= 72/92 = 0.7826
= P ( Z <0.7826) From Standard Normal Table
= 0.78307
P(300 < X < 400) = 0.78307-0.38043 = 0.4026