Question 300757: 2. Assume the 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 the 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 a 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 the 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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 2. Assume the 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 the University of Maryland researchers).
a. If you have a body temperature of 99.00 °F, what is your percentile score?
Find the z-score for 99.
Find the percent of population with a z-score that is less than
the z-score for 99.
The is the percentile score of 99
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b. Convert 99.00 °F to a standard score (or a z-score).
You've had to do that in the "a" problem.
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c. Is a body temperature of 99.00 °F unusual? Why or why not?
If its z-score is less than -2 or more than +2 it is considered
to be "unusual".
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d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower?
Find the z-score of 97.98 using mean = 98.2 and std = 0.62/sqrt(50)
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e. A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude?
Find the z-score of 101 and make your conclusion.
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f. What body temperature is the 95th percentile?
Find the z-score with a left tail of 0.95.
Convert to a temperature score using temp = z*s+u
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g. What body temperature is the 5th percentile?
Findt the z-score with a left tail of 5%.
Convert to a temperature score using temp = z*s+u
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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?
Find the z-score of 100.6.
Find the percent population above that z-score.
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Does this percentage suggest that a cutoff of 100.6 °F is appropriate?
Make your judgement.
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Cheers,
Stan H.
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