SOLUTION: A drug test is accurate 96% of the time. If the test is given to 1900 people who have not taken drugs, what is the probability that at least 79 will test positive?

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Question 1169578: A drug test is accurate 96% of the time. If the test is given to 1900 people who have not taken drugs, what is the probability that at least 79 will test positive?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
n = 1900
p = 0.04
q = 0.96

MEAN = np = (1900)(0.04) = 76
SD = sqrt%28npq%29 = sqrt%281900+%2A+0.04+%2A+0.96%29 = sqrt%2872.96%29 = 8.5417

P(x ≥ 79) ---> P(x > 79 - 0.5) ---> P(x > 78.5)

z = %2878.5+-+76%29%2F8.5417 = 2.5%2F8.5417 = 0.29

Looking at a z-table, you will see that there is a 0.6141 probability that fewer than 79 people test positive. This means there is a 0.3858 probability that 79 or more people ("at least 79") test positive.