The average age of doctors in a certain hospital is 48.0 years old with a standard deviation of 6.0 years. If 25 doctors are chosen at random for a committee, find the probability that the mean age of those doctors
Is less than 48.60 years. Assume that the variable is normally distributed.
A) 0.3085
B) 0.5715
C) 0.6675
D) 0.6915

Question

Quizplus · Accepted Answer

The standard error of the mean is calculated as the standard deviation divided by the square root of the sample size: 6.0 / √25 = 1.2. The z-score for a mean age of 48.60 is (48.60 - 48.0) / 1.2 = 0.5. Using the standard normal distribution table, the probability corresponding to a z-score of 0.5 is approximately 0.6915.

The Average Age of Doctors in a Certain Hospital Is