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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

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JeanaShupp

Answer: 0.00102%

Step-by-step explanation:

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

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

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

[tex]z=\dfrac{x-\mu}{s}[/tex]

For x= 100.6, [tex]z=\dfrac{100.6-98}{0.61}=4.26229508197\approx4.26[/tex]

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

P(x>100.6)=[tex]P(Z>4.26)=0.0000102=0.00102\%[/tex]

Hence, the required probability = 0.00102%

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