Question

Assume that human body temperatures are normally distributed with a mean of 98.19 degrees Fahrenheit and a standard deviation of 0.64 degrees Fahrenheit. A hospital uses 100.6 degrees Fahrenheit as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 degrees Fahrenheit is appropriate?

Answer 1

To determine the percentage of normal and healthy persons considered to have a fever, calculate the z-score for 100.6 using the normal distribution formula. Find the area to the right of the z-score using a z-table or calculator. The small percentage suggests that using 100.6 degrees Fahrenheit as the cutoff for a fever is appropriate.

Step-by-step explanation:

To determine the percentage of normal and healthy persons considered to have a fever, we need to find the proportion of people with body temperatures above 100.6 degrees Fahrenheit. Using the normal distribution with a mean of 98.19 and a standard deviation of 0.64, we can calculate the z-score for 100.6. The z-score formula is (x - mean) / standard deviation. Plugging in the values, we get a z-score of (100.6 - 98.19) / 0.64 = 3.75.

We can then use a z-table or a calculator to find the area to the right of the z-score of 3.75. The area under the curve represents the percentage of people with body temperatures above 100.6 degrees Fahrenheit. From the z-table or calculator, the area is approximately 0.0001 or 0.01%, which is a very low percentage.

This suggests that using 100.6 degrees Fahrenheit as the cutoff for a fever is appropriate since it corresponds to a very small percentage of the population with normal and healthy body temperatures.