A drug tester claims that a drug cures a rare skin disease 7

A drug tester claims that a drug cures a rare skin disease 70% of the time. The claim is checked by testing the drug on 100 patients. If at least 64 patients are cured, the claim will be accepted. Find the probability that the claim will be rejected assuming that the manufacturer\'s claim is true. Use the normal distribution to approximate the binomial distribution if possible.

The probability is=(Round to four decimal places as needed.)

Solution

We first get the z score for the critical value:          
          
x = critical value =    63.5      
u = mean = np =    70      
          
s = standard deviation = sqrt(np(1-p)) =    4.582575695      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -1.418416287      
          
Thus, the left tailed area is          
          
P(z >   -1.418416287   ) =    0.921965368 [ANSWER]