For after-hours emergencies,

Question

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?

Answer 1

Out of 80 randomly sampled calls, we would expect 24 of them to have no corresponding messages. The probability that a randomly selected call has no corresponding message is 24/80 or 3/10. The probability that one randomly selected call will have a corresponding message with it is 56/80 or 7/10.

 

You asked what the probability is for more than 30 calls with no corresponding messages out of a total of 80 randomly selected calls. However, we cannot determine this probability, other than to say, based on the strict 30 percent won't assertion, the probability is zero. If you have more than one sampling and some summary statistics, then we can make some different predictions.