Question

Consider a random variable X that is normally distributed. Complete (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) (a)If a random variable X is normally distributed, what will be the shape of the distribution of the sample mean? Normal O Skewed left O Skewed right O Cannot be determined (b) If the mean of a random variable X is 30, what will be the mean of the sampling distribution of the sample mean? (c) As the sample size n increases, what happens to the standard error of the mean? A. The standard error of the mean remains the same. OB. The standard error of the mean increases O C. The standard error of the mean decreases

Answer 1

a) The distribution of the sample mean will be normal. b) The mean of the sampling distribution of the sample mean will be 30. c) As the sample size increases, the standard error of the mean decreases.

Step-by-step explanation:

a) If a random variable X is normally distributed, the distribution of the sample mean will also be normal. The central limit theorem states that as the sample size increases, the distribution of the sample mean approaches a normal distribution.

b) The mean of the sampling distribution of the sample mean will be the same as the mean of the random variable X, which is 30.

c) As the sample size increases, the standard error of the mean decreases. The standard error of the mean is equal to the standard deviation of the population divided by the square root of the sample size.