A new medical test provides a false positive result for Hepatitis 2% of the time. That is, a perfectly healthy subject being tested for Hepatitis will test as being infected 2% of the time. In research, the test is given to 30 healthy (not having Hepatitis) subjects. Let X be the number of subjects who test positive for the disease.
a) What is the probability that all 30 subjects will appropriately test as not being infected?
b) What are the mean and standard deviation of X?
c) To what extent do you think this is a viable test to use in the field of medicine?
a) What is the probability that all 30 subjects will appropriately test as not being infected?
b) What are the mean and standard deviation of X?
c) To what extent do you think this is a viable test to use in the field of medicine?
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Binomial distribution is used.
P(not infected) = 100%-2% = 98% = 0.98
q = 1-p = 1-0.98 = 0.02
n = 30
P(r) = nCr*q^(n-r)*p^r
a) Required probability = P(r=30) = 30C30*0.02^0*0.98^30
= 1*1*0.5455
= 0.5455
b) Mean = np = 30*0.98 = 29.4
Standard deviation = sqrt (npq)
= sqrt (30*0.98*0.02)
= 0.7668
P(not infected) = 100%-2% = 98% = 0.98
q = 1-p = 1-0.98 = 0.02
n = 30
P(r) = nCr*q^(n-r)*p^r
a) Required probability = P(r=30) = 30C30*0.02^0*0.98^30
= 1*1*0.5455
= 0.5455
b) Mean = np = 30*0.98 = 29.4
Standard deviation = sqrt (npq)
= sqrt (30*0.98*0.02)
= 0.7668