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

Question

Quizplus · Accepted Answer

First, we need to check if the sample size is large enough to use a normal approximation. Since np = 300 * 0.9 = 270 >= 10 and n(1-p) = 300 * (1-0.9) = 30 >= 10, we can use the normal approximation to the binomial distribution. 
Next, we need to calculate the mean and standard deviation of the sample, assuming that the distribution of the sample proportion is normal: 
mean = np = 270 
standard deviation = sqrt(np(1-p)) = sqrt(300*0.9*0.1) = 4.74 
Finally, we can use the normal distribution to find the probability that more than 265 patients will be relieved of nasal congestion: 
z = (265.5 - 270) / 4.74 = -0.95 
P(z > -0.95) = 0.8078 (using a standard normal table or calculator) 
Therefore, the probability that more than 265 patients will be relieved of nasal congestion is 0.8078 or approximately 81%.

A New Drug Has Been Developed That Is Found to Relieve