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 x-bar 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) x-bar is approximately normally distributed.

B) The distribution of x-bar is uniform.

C) x-bar is normally distributed.

D) None of the above statements is true.

I am thinking it is uniformed because of the sample size of 32 which means if this was to be on a dotplot, there would only be one plotted data because the dice was rolled 32 times.

No. X-bar is the running mean. Each time a number is thrown, it changes the mean. It should approximate a normal distribution.

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  1. ANSWER: x̅ is approximately normally distributed.

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