I do not understand how to put the answer in the form of fra
I do not understand how to put the answer in the form of fraction.
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 |
Solution
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 103.39
u = mean = 101.7
s = standard deviation = 0.563
Thus,
z = (x - u) / s = 3.001776199
Thus, using a table/technology, the right tailed area of this is
P(z > 3.001776199 ) = 0.001342047 [answer]
*********************
b)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 101.59
x2 = upper bound = 102.21
u = mean = 101.7
s = standard deviation = 0.563
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.195381883
z2 = upper z score = (x2 - u) / s = 0.905861456
Using table/technology, the left tailed areas between these z scores is
P(z < z2) = 0.817495406
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.817495406 [answer]

