A clinic took temperature readings of 250 flu patients over a weekend and discov

Question

A clinic took temperature readings of 250 flu patients over a weekend and discovered the temperature distribution to be Gaussian, with a mean of 101.70°F and a standard deviation of 0.5630. Use this normal error curve area table to find the following values. (a) What is the fraction of patients expected to have a fever greater than 103.39°F?

(b) What is the fraction of patients expected to have a temperature between 101.59°F and 102.21°F?

Ordinate and Area for a Normal Error Curve

z = (x – )/
The area refers to the area between z = 0 and z = the table value.

|z| y Area 0.0 0.3989 0.0000 0.1 0.3970 0.0398 0.2 0.3910 0.0793 0.3 0.3814 0.1179 0.4 0.3683 0.1554 0.5 0.3521 0.1915 0.6 0.3332 0.2258 0.7 0.3123 0.2580 0.8 0.2897 0.2881 0.9 0.2661 0.3159 1.0 0.2420 0.3413 1.1 0.2179 0.3643 1.2 0.1942 0.3849 1.3 0.1714 0.4032 1.4 0.1497 0.4192 1.5 0.1295 0.4332 1.6 0.1109 0.4452 1.7 0.0941 0.4554 1.8 0.0790 0.4641 1.9 0.0656 0.4713 2.0 0.0540 0.4773 2.1 0.0440 0.4821 2.2 0.0355 0.4861 2.3 0.0283 0.4893 2.4 0.0224 0.4918 2.5 0.0175 0.4938 2.6 0.0136 0.4953 2.7 0.0104 0.4965 2.8 0.0079 0.4974 2.9 0.0060 0.4981 3.0 0.0044 0.498650 3.1 0.0033 0.499032 3.2 0.0024 0.499313 3.3 0.0017 0.499517 3.4 0.0012 0.499663 3.5 0.0009 0.499767 3.6 0.0006 0.499841 3.7 0.0004 0.499904 3.8 0.0003 0.499928 3.9 0.0002 0.499952 4.0 0.0001 0.499968 0 0.5

Explanation / Answer

Given:

The Gussian mean = 101.70F

Standard deviation = 0.5630

a) What is the fraction of patients expected to have a fever greater than 103.39°F

standard deviations above the mean = 103.39 - 101.7 / 0.5630 = 1.69 / 0.5630 = 3.00

So the chance for this will be 0.0033 = 0.33 %

b) What is the fraction of patients expected to have a temperature between 101.59°F and 102.21°F

Finding the probability to the right of the low score and to the left of the high score and taking the difference will give the probability in between.

Probability right of 101.59 is: 101.59 -101.70 / 0.5630 =-0.11/0.5630 = -0.1953 standard deviations away.(Negative, since it is below the mean) Probability of this is0.3989

Probability left of 102.21 is: 102.21-101.7 =0.51/0.5630=0.905 standard deviations away. Probability of this is 0.242

0.3989 - 0.242 =.1569. 15.69%

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