21 A new drug has been developed that is found to relieve na

21. A new drug has been developed that is found to relieve nasal congestion in 90 percent of those with the condition. The new drug is administered to 300 patients with the condition. What is the probability that more than 265 will be relieved of nasal congestion? A.) 0.0916 B. 0.1922 C. 0.8078 D. 0.3078

Solution

We first get the z score for the critical value:          
          
x = critical value =    265.5      
u = mean = np =    270      
          
s = standard deviation = sqrt(np(1-p)) =    5.196152423      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -0.866025404      
          
Thus, the left tailed area is          
          
P(z <   -0.866025404   ) =    0.8078 [ANSWER, C]