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

Answer:

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

Step-by-step 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 = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

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

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

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