Which of the following one choice is true regarding the probability distribution

Question

Which of the following one choice is true regarding the probability distribution of Xbar, for a sufficiently large sample size?

a) depends on the value of M(mean), but not the value of O (standard deviation)

b) depends on the value of O, but not the value of M

c) It has the same shape, mean, and standard deviation as the population distribution

d) It has the same shape and mean as the population distribution with a smaller standard deviation

e) It has a normal distribution, with the same mean and standard deviation as the population distribution

Explanation / Answer

The correct option is D

Explanation:

Regarding the probability distribution of Xbar, for a sufficiently large sample size ,the standard deviation of the sample means (known as the standard error of the mean) will be smaller than the population standard deviation and will be equal to the standard deviation of the population divided by the square root of the sample size.

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