Let $x$ represent the number which shows up when a balanced die is rolled. Then $x$ is a random variable with a uniform distribution. Let $\bar { x }$ denote the mean of the numbers obtained when the die is rolled 32 times. For samples of size 32, which of the following statements concerning the sampling distribution of the mean is true?
A)$\bar { x }$ is normally distributed.
B) $\bar { x }$ is approximately normally distributed.
C) The distribution of $\bar { x }$ is uniform.
D) None of the above statements is true.

Question

Let $x$ represent the number which shows up when a balanced die is rolled. Then $x$ is a random variable with a uniform distribution. Let $\bar { x }$ denote the mean of the numbers obtained when the die is rolled 32 times. For samples of size 32, which of the following statements concerning the sampling distribution of the mean is true?  
A)$\bar { x }$ is normally distributed.
B) $\bar { x }$ is approximately normally distributed.
C) The distribution of $\bar { x }$ is uniform.
D) None of the above statements is true.

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, provided the sample size is sufficiently large. In this case, with 32 rolls of a die, the sample size can be considered large enough for the approximation to be valid.

Let xxx Represent the Number Which Shows Up When a Balanced Die

Let $x$ Represent the Number Which Shows Up When a Balanced Die