According to Manhattan Research, 44% of physicians surveyed said they communicate with patients through e-mail. A random sample of 120 physicians was selected. What is the probability that 50 or more from this sample e-mail their patients?

Question

Quizplus · Accepted Answer

This is a binomial probability problem where we are looking for the probability of 50 or more successes (physicians emailing their patients) out of 120 trials (physicians), with the success probability of 0.44 for each trial. The calculation of this probability directly or through normal approximation (given the large sample size) would yield a result closest to the option A) 0.6950. This option represents the cumulative probability of having from 50 to 120 physicians emailing their patients, which aligns with the higher probability side of the binomial distribution centered around its mean (0.44 * 120 = 52.8).

According to Manhattan Research, 44% of Physicians Surveyed Said They