The average age of doctors in a certain hospital is 45.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 4.0 years. If 16 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 45.5 years. Assume that the variable is normally distributed.
A) 19.1%
B) 30.9%
C) 61.2%
D) 69.1%

Question

Quizplus · Accepted Answer

The standard error of the mean is 4.0/sqrt(16) = 1.0. The z-score for 45.5 is (45.5 - 45.0) / 1.0 = 0.5. Using the standard normal distribution table, the probability of a z-score less than 0.5 is approximately 0.6915, or 69.1%.

The Average Age of Doctors in a Certain Hospital Is