Let X denote the outcome of rolling a die a. Construct a graph of the (0) probab
ID: 3350057 • Letter: L
Question
Let X denote the outcome of rolling a die a. Construct a graph of the (0) probability distribution of X and you would get if you could roll the die an infinite number of times.) b. The probability distribution of X has mean 3.50 an for (i) n 2, (i) n -30. What is the effect of n on the sampling distribution? i) sampling distribution of the sample mean for n 2. (You can think of (0) as the population distribution d standard deviation 1 71. Find the mean and standard deviation of the sampling distribution of the sample mean a. (1) Which graph shows the probability distribution of X? O A. OB O C. 0.1 0.2 0.15 0.1 a 0.05- 12 3456 1.1 3.50 5.9 0.1 3.50 6.9 Outcome i) Which graph shows the sampling distribution of the sample mean for n -2? OA. 0.1 0.2 0.2 2 0.1 005 2 0.1 123456 123456 0 1 3.50 69 123456 OutoomeExplanation / Answer
(a) (i) Option D shows us the probability distribution of X.
(ii) Option C shows us the sampling distribution of the sample mean of X.
(b)(i) For n = 2, the mean is 3.50 and the standard deviation = 1.71/sqrt(2) = 1.21
(ii) For n = 30, the mean is 3.50 and the standard deviation = 1.71/sqrt(30) = 0.31
As n increases, the mean of the sampling distribution remains constant and the standard deviation of the sampling distribution decreases.
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