The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of ten 18-year-old men will be between 67 and 68 inches? $$\bar { x }$$
A)0.3531
B)0.6469
C)0.1469
D)0.7062
E)0.3961

Question

Quizplus · Accepted Answer

The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size. In this case, the mean of the sample means will be 68 inches, and the standard deviation of the sample means will be 3 inches / sqrt(10) = 0.949 inches. The probability that the average height of a sample of ten 18-year-old men will be between 67 and 68 inches is the area under the normal curve between z = -1.05 and z = 1.05. This area is equal to 0.3531.

The Heights of 18-Year-Old Men Are Approximately Normally Distributed with Mean