Suppose that the blood sugar levels of diabetic subjects and nondiabetic subjects
form two independent normally distributed populations, the means of which are
140 mg/100 ml and 90 mg/100 ml, respectively. The standard deviations are 25
mg/100 ml for both populations. It is known that 5% of the population are diabetic.
Whenever a subject’s blood sugar level measured is 140 mg/100 ml or above, we
say that the result of the blood test is positive. On a given day two subjects were
recruited for reasons other than suspected diabetes.
(a) If a subject’s blood test is positive, what is the probability that the subject
actually is nondiabetic ?
(b) If both subjects’ blood tests are positive, what is the probability that at least
one of them actually is nondiabetic ?
(c) If a subject is tested twice consecutively and both results are positive, what is
the probability that the subject actually is nondiabetic ?
\”Blood sugar test\” probability
2010-02-28 9:45 pm
回答 (2)
2010-03-02 11:42 pm
✔ 最佳答案
(a): Pr (nondiabetic | positive) = 0.95 x Pr {Z > [(140 – 90) / 25]} = 0.95 x 0.0228 = 0.0216(b):
Pr (diabetic | positive) = 0.05 x Pr {Z > [(140 – 140) / 25]} = 0.05 x 0.5 = 0.025
Pr (at least one of them is nondiabetic | both are positive) = 0.0216 x 0.0216 + 2 x 0.0216 x 0.025 = 0.0005 + 0.0011 = 0.0015
(c): Pr (nondiabetic | twic positive) = 0.95 x 0.02282 = 0.0005
2010-03-03 10:14:15 補充：
why is it wrong?
2010-03-10 08:31:03 補充：
why answer c should be same as answer a?
the probability of a positive results should not be equal to that of twice positive results
If you get a positive results, your probability of nondiabetic is A
If you get twice positive results your probability of nondiabetic is C
2010-03-10 08:31:47 補充：
Obviously C is much smaller than A
Otherwise, why I need to take the second test if the second test could not improve the probability
2010-03-03 2:44 am
Wrong answer.
2010-03-04 21:52:26 補充：
Beacuse ans of c) is obviusly same as a).
a)0.4624
b)0.7129
c)same as a)
2010-03-13 15:26:41 補充：
c)
I mean a question can be used to tested whether you are purely using formula.
In the question, we have a test is 100% correct. What we going to discuss is that the what test result will indicate, that is the probability that he or she is a diabetic patient. See what I mean?
2010-03-04 21:52:26 補充：
Beacuse ans of c) is obviusly same as a).
a)0.4624
b)0.7129
c)same as a)
2010-03-13 15:26:41 補充：
c)
I mean a question can be used to tested whether you are purely using formula.
In the question, we have a test is 100% correct. What we going to discuss is that the what test result will indicate, that is the probability that he or she is a diabetic patient. See what I mean?
收錄日期: 2021-04-23 18:24:56
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