Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is:
A)0.4332.
B)0.0668.
C)0.0987.
D)0.9013.

Question

Quizplus · Accepted Answer

We can use the Central Limit Theorem to approximate the distribution of sample means as normal with a mean of 75 and a standard deviation of 12/√36=2. Thus, we want to find P(Z>(78-75)/2) = P(Z>1.5) ≈ 0.0668, where Z is a standard normal random variable.

Given an Infinite Population with a Mean of 75 and a Standard