Question

Assume that human body temperatures are normally distributed with a mean of 98.2°F and a standard deviation of 0.63°F a hospital uses it 100.6°F as the lowest temperature considered to be a fever what percentage of normal and healthy person would be considered to have a fever does this percentage suggested a cut off of 100.6°F is appropriate B physicians want to select a minimum temperature for requiring for the medical test what should the temperature be if we want only 5% of healthy people to exceed it

Answer 1

Mean temperature

Standard deviation

Let variable x denotes the temperature reading for a normal and healthy person

Percentage of normal and healthy persons would be considered to have fever :

Z-score for (x=100.6):

Hence,

From normal distribution table,

Therefore, Percentage of normal and healthy persons would be considered to have fever

The above percentage is quite low which implies that it is very unlikely that person with temperature 100.6 or more be considered as normal. Hence, the cut-off seems appropriate

Part:B:

From normal distribution table, value of 'z-score' having area under the normal curve to the right of that z-score equal to 0.05 is given by : z=1.645

Hence value of temperature, if we want only 5% of healthy people to exceed it = 99.24