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 $348. Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $87. Answer questions 3 to 6 about the cost of a hospital emergency room visit for this medical service. What is the probability that the cost will be less than $500? g

Answer 1

Probability that the cost will be less than $500 is 0.95994 .

Explanation:

We are given that Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $348 with a standard deviation of $87.

Let X = cost of a hospital emergency room visit for this medical service

So, X ~ N(
`\mu=348, \sigma^(2) =87^(2)`)

The standard normal z score distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

(a) Probability that the cost will be less than $500 = P(X < $500)

P(X < 500) = P(
`(X-\mu)/(\sigma)` <
`(500-348)/(87)` ) = P(Z < 1.75) = 0.95994 {from z table}

Therefore, the probability that the cost will be less than $500 is 0.95994 .