For after-hours emergencies, doctors often use a messaging/paging service to allow patients to contact them.If it is known that 30% of the patients who call the messaging service fail to leave a message for the doctor, what is the probability that out of 80 randomly sampled calls, more than 30 will fail to leave a message?
A) 0.0512
B) 0.9279
C) 0.3750
D) 0.0721

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution, where:
- n = 80 (number of trials)
- p = 0.3 (probability of failure)
- q = 0.7 (probability of success)

We need to find the probability that more than 30 calls fail to leave a message. This can be written as:

P(X > 30) = 1 - P(X ≤ 30)

Using the binomial distribution formula or a calculator, we can calculate P(X ≤ 30) = 0.9279.

Therefore, P(X > 30) = 1 - 0.9279 = 0.0721.

Hence, the answer is D.

For After-Hours Emergencies, Doctors Often Use a Messaging/paging Service to Allow