Question

Assume that human body temperatures are normally distributed with a mean of 98.22 degrees Upper F 98.22°F and a standard deviation of 0.61 degrees Upper F0.61°F. a. A hospital uses 100.6 degrees Upper F100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a​ fever

Answer 1

Answer: 0.00102%

Step-by-step explanation:

Given : Human body temperatures are normally distributed with a mean of $\mu=98^{\circ}F$and a standard deviation of $s=0.61^{\circ}F$

A hospital uses $100.6^{\circ}F$ as the lowest temperature considered to be a fever.

Let x be the random variable that represents the human body temperatures.

$z=\dfrac{x-\mu}{s}$

For x= 100.6, $z=\dfrac{100.6-98}{0.61}=4.26229508197\approx4.26$

Using normal distribution table for z-values for right-tailed area ,

P(x>100.6)=$P(Z>4.26)=0.0000102=0.00102\%$

Hence, the required probability = 0.00102%