Assume that human body temperatures are approximately normally distributed with
ID: 3141923 • Letter: A
Question
Assume that human body temperatures are approximately normally distributed with a mean of 98 2 degree F and a standard deviation of 0.62 degree F. a. Suppose that a person monitoring their body temperature takes their temperature and records the value Estimate the probability that person has a body temperature of 97.9 degree F. a Suppose that a person monitoring their body temperature takes a sample of 10 measurements, one per day at the same time over the next 10 days. Estimate the probability that persons has a body temperature of 99 degree F. c. University Hospital in New Orleans uses 100 6 degree F as the lowest temperature considered to be a fever. What percentage of normal healthy persons would be considered to have a fever? (Give answer as a percentage with 1 decimal place accuracy). d. Based on your answer in part a., does this percentage suggest that a cutoff of 100.6 degree F is appropriate? E. As a physician, you want to select a minimum temperature for requiring further medical tests. What should that temperature be, if you want only 5% of healthy people to exceed it?Explanation / Answer
Mean = u = 98.2
SD= 0.62
e) If I want only 5% of the healthy people to exceed it, I will go for a normal distribution curve and find its z-value at z=0.45 on a one-sided tail;
since the other side of the tail will be entire area of 0.5 since we are only to take people who exceed the temperature;
For z= 1.645, the area of the curve is coming out to be = 0.45;
This means that at z=1.45, only 5% of people fall under the range greater than z=1.645
if z=1.645 then
x-u/ SD = 1.645;
x-u = 1.645*0.62= 1.0199
x= u+1.0199 = 98.2+1.0199 = 99.2199
Thus, only 5% of healthy people will exceed a temperature of 99.2199 degrees;