Group blood testing During World War II it was necessary to administer blood tests to large numbers of recruits. There are two standard ways to administer a blood test to N people. In method 1, each person is tested separately. In method 2, the blood samples of x people are pooled and tested as one large sample. If the test is negative, this one test is enough for all x people. If the test is posi- tive, then each of the x people is tested separately, requiring a total of x + 1 tests. Using the second method and some probabil- ity theory it can be shown that, on the average, the total number of tests y will be y = N(1 − g²¹ + 1). - qt = With q 0.99 and N = 1000, find the integer value of x that mini- mizes y. Also find the integer value of x that maximizes y. (This second result is not important to the real-life situation.) The group testing method was used in World War II with a savings of 80% over the individual testing method, but not with the given value of q.
Group blood testing During World War II it was necessary to administer blood tests to large numbers of recruits. There are two standard ways to administer a blood test to N people. In method 1, each person is tested separately. In method 2, the blood samples of x people are pooled and tested as one large sample. If the test is negative, this one test is enough for all x people. If the test is posi- tive, then each of the x people is tested separately, requiring a total of x + 1 tests. Using the second method and some probabil- ity theory it can be shown that, on the average, the total number of tests y will be y = N(1 − g²¹ + 1). - qt = With q 0.99 and N = 1000, find the integer value of x that mini- mizes y. Also find the integer value of x that maximizes y. (This second result is not important to the real-life situation.) The group testing method was used in World War II with a savings of 80% over the individual testing method, but not with the given value of q.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:26. Group blood testing During World War II it was necessary to
administer blood tests to large numbers of recruits. There are two
standard ways to administer a blood test to N people. In method 1,
each person is tested separately. In method 2, the blood samples
of x people are pooled and tested as one large sample. If the test is
negative, this one test is enough for all x people. If the test is posi-
tive, then each of the x people is tested separately, requiring a
total of x + 1 tests. Using the second method and some probabil-
ity theory it can be shown that, on the average, the total number
of tests y will be
x − x(₁-0 + 1)
= N(1-
y =
qt
=
With q = 0.99 and N 1000, find the integer value of x that mini-
mizes y. Also find the integer value of x that maximizes y. (This
second result is not important to the real-life situation.) The group
testing method was used in World War II with a savings of 80% over
the individual testing method, but not with the given value of q.
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