4.6 – Based on the sample results below, assume that human body temperature are
ID: 3126309 • Letter: 4
Question
4.6 – Based on the sample results below, assume that human body temperature are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F.
a) Bellevue Hospital in New York City uses 100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6°F is appropriate?
Temperature Day . Subject Age Smoke AM 97.0 98.0 98.4 98.4 98.8 98 2 98.6 96.6 98.8 98.2 97.8 97.6 98.0 97.6 98.6 98.6 98.8 97.0 98.6 974 97.0 98.2 98.0 98.0 976 98.8 972 97.6 970 97.7 98.2 96.8 97.3 98.2 97.8 97.4 982 98.9 97.8 98.6 99.0 974 97.5 974 973 97.5 976 978 982 98.2 98.5 99.0 99.5 97.8 98.3 98.0 99.4 98.2 98.0 98.0 99.0 98.6 98.4 (continued) 4965 .5 .3 .6 2 .6 .7 98-98 98 98 99 98 98 98 98 98 98 8 6 97 97 98 97 97 98 98 98 98 98 97 -900 980 900 99 98 98 98 98 98 98 98 98 97:: 98 980 3 53, 97 98 98 99 97 97 97 996 and : 97 98 980 97 980 0662 .4 .6 .2 .0 .8- AM 0 4 8 0 0 6 0 8 6 6 2 .6 .6 .0 .4 0 6 2 0 0 4 1 0 8 2 .8 2 .8 0 4 4 5 89830 98 9 9 9 9 96 97 96 96 96 96 97 98 97 97 98 97 97 97 98 97 96 96 98 96 98 97 98 97 99 97 97 97 97 97 97 98 98 0 .6 8 0 8 8 6 6 6 8 0 2 0 0 0 2 2 ay 12 98 97 98 98 98 98 97 98 98 98 98 98 98 98 97 97 98 -125 98 99 98 97 97 97 98-97 990 97 97 98 97 98-98 98 4 97-98 .6 .4 2 2 2 6 4 4 2 4 8 See M M M M M M M M MMMMMMMMMMFFMFMMMFMMMMMMMMMMMMMMMMFMMFMMM Age 22 23 22 19 18 20 27 19 24 35 25 25 35 21 33 24 18 22 20 30 29 18 31 28 27 21 30 27 32 33 23 29 25 31 25 28 30 33 28 22 21 30 22 22 20 33 123456789 10 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 2 3 4 5 6 7 48 49Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 100.6
u = mean = 98.2
s = standard deviation = 0.62
Thus,
z = (x - u) / s = 3.870967742
Thus, using a table/technology, the right tailed area of this is
P(z > 3.870967742 ) = 5.42021*10^-5 = 0.00542% [ANSWER]
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Yes it is appropriate, becasue very few healthy people will be diagnosed as someone with fever. [CONCLUSION]
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