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
E) None of the choices are correct

Question

Quizplus · Accepted Answer

The probability of a patient being relieved of nasal congestion is 0.9. The probability of more than 265 patients being relieved of nasal congestion is the complement of the probability of 265 or fewer patients being relieved of nasal congestion. The probability of 265 or fewer patients being relieved of nasal congestion is the sum of the probabilities of 0, 1, 2, ..., 265 patients being relieved of nasal congestion. This sum can be calculated using the binomial distribution. The probability of more than 265 patients being relieved of nasal congestion is therefore 1 - the sum of the probabilities of 0, 1, 2, ..., 265 patients being relieved of nasal congestion. This probability is approximately 0.8078.

A New Drug Has Been Developed That Is Found to Relieve