Assume that body temperatures of healthy adults are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F (based on data from University of Maryland researchers).
a. If you have a body temperature of 99.00°F, what is your percentile score?
b. Convert 99.00°F to a standard score (or z-score).
c. Is a body temperature of 99.00°F "unusual"? Why or why not?
d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98°F or lower?
e. A person's body temperature is found to be 101.00°F. Is this result "unusual"? Why or why not? What should you conclude?
f. What body temperature is the 95th percentile?
g. What body temperature is the 5th percentile?
h. Bellevue Hospital in New York City uses 100.6°F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6°F is appropriate?
i. If, instead of assuming that the mean body temperature is 98.20°F, we assume that the mean is 98.60°F (as many people believe), what is the chance of randomly selecting 106 people and getting a mean of 98.20°F or lower? (Continue to assume that the standard deviation is 0.62°F.) University of Maryland researchers did get such a result. What should we conclude?