Question 453907
A new drug has been tested and is found to have a cure rate of 80%. 
The drug is given to a random sample of 100 patients for a further test. 
Using a normal approximation to the binomial distribution, find the probability that: 
a) at least 75 patients will be cured
mean = np = 100*0.80 = 80
std = sqrt(npq) = sqrt(80*0.2) = 4
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z(74.5) = (74.5-80)/4 = -1.1 
z(100.5) = (100.5-80)/4 = 20.5/4 = 5.125
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P(75<= x <=100) = P(-1.1< z < 5.125) = 0.8643
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b) exactly 80 patients will be cured 
z(79.5) = (79.5-80)/4 = -0.125 
z(80.5) = (80.5-80)/4 = +0.125
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P(x = 80) = P(-0.125< z <0.125) = 0.0995
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Cheers,
Stan H.