Question

1. 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.

1. What is the probability that the cost will be more than $500?

2. What is the probability that the cost will be less than $250?

3. What is the probability that the cost will be between $300 and $400?

4. If the cost to a patient is in the lower 8% of charges the cost of this patient’s emergency room visits?

Answer 1

Solution :

a):- What is the probability that the cost will be more than $500? (to 4 decimals)

z = (x - µ) /σ
z = (500 - 328) /92 = 1.869565
from z-score table
P( x ≤ 500) = 0.969228
P(x > 500) = 1 - P( x ≤ 500)
P(x > 500) = 0.0308

b):- What is the probability that the cost will be less than $250? (to 4 decimals)

z = (x - µ) /σ
z = (250 - 328) /92 = -0.8478261
z = (500 - 328) /92 = 1.869565
from z-score table
P( x < 250) = 0.1983

c):- What is the probability that the cost will be between $300 and $400? (in inches, to 4 decimals)

z = (300 - 328) /92 = -0.30435
P( x ≤ 300) = 0.380431
z = (400 - 328) /92 = 0.782609
P( x ≤ 400) = 0.783072
P( 300 < x < 400 )
= 0.783072 - 0.380431
= 0.402641

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? (to 2 decimals)

p = 8% = 0.08
then z = -1.40507
z = (x - µ) /σ
x = µ + σz
x = 328 + 92(-1.40507)
x = $198.73

Hope its helpful...please like the answer...