A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean that is at least equal to the population mean?
A) .50
B) equal to the probability of selecting a sample mean that is at most equal to the population mean
C) .50 and equal to the probability of selecting a sample mean that is at most equal to the population mean
D) none of these

Question

Quizplus · Accepted Answer

The probability of selecting a sample mean that is at least equal to the population mean is .50 because, by the Central Limit Theorem, the sampling distribution of the sample mean is normally distributed if the sample size is large enough (which is generally considered to be the case for n > 30). This means the distribution is symmetric around the population mean, making the probability of selecting a sample mean at least equal to the population mean the same as the probability of selecting a sample mean at most equal to the population mean, both being .50.

A Researcher Selects a Sample of 49 Participants from a Population