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 visitis 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.Required: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?

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Assume a normal distribution :

Mean (m) = 328

Standard deviation (sd) = 92

To obtain Zscore :

Zscore = (x - m) / sd

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

x = $500

Zscore = (500 - 328) / 92 = 172 / 92 = 1.869 = 1.87

1 - p(Z < 1.87) = 1 - 0.9693 = 0.0307

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

x = $250

Zscore = (250 - 328) / 92 = - 78 / 92 = - 0.8478 = - 0.85

p(Z < - 0.85) = 0.1977

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

x = 300

Zscore = (300 - 328) / 92 = - 28/ 92 = -0.30

p(Z < - 0.3) = 0.3821

x = 400

Zscore = (400 - 328) / 92 = 72/ 92 = 0.783

p(Z < 0.783) = 0.7823

0.7823 - 0.3821 = 0.4002

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?

Probability is lower 8%

P (Z < Zscore) = 0.08

Zscore of 0.08 corresponds to - 1.41 on the z table

Zscore = (x - m) / sd

-1.41 = (x - 328) / 92

-129.72 = x - 328

-129.72 + 328 = x

x = 198.28