Question

g A visit to a hospital emergency room for something as simple as a sore throat could have a mean cost of $328. Assume that this cost is normally distributed with a standard deviation of $82. If you want to be in the bottom 50%, what will be the cut-off dollar amount

Answer 1

Answer:

The cut-off dollar amount is $328.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean cost of $328, standard deviation of $82.

This means that $\mu = 328, \sigma = 82$

If you want to be in the bottom 50%, what will be the cut-off dollar amount?

The 50th percentile, which is X when Z has a pvalue of 0.5. So X when Z = 0.

$Z = \frac{X - \mu}{\sigma}$

$0 = \frac{X - 328}{82}$

$X - 328 = 0*82$

$X = 328$

The cut-off dollar amount is $328.