Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height between 68
And 70 inches.
A)0.9958
B)0.9979
C)0.0021
D)0.9015

Question

Quizplus · Accepted Answer

The probability that the mean height of 64 randomly selected men falls between 68 and 70 inches can be found using the standard normal distribution formula for a sample mean. The standard error (SE) of the mean is the standard deviation (σ) divided by the square root of the sample size (n), which is 2.8 / sqrt(64) = 0.35. The Z-scores for 68 and 70 inches are (68 - 69) / 0.35 = -2.86 and (70 - 69) / 0.35 = 2.86, respectively. Looking these Z-scores up in a standard normal distribution table or using a calculator gives a probability between them, which is very close to 1, indicating a very high likelihood. Choice A, 0.9958, is the closest to this theoretical probability, making it the correct answer.

Assume That the Heights of Men Are Normally Distributed with a Mean