# Question

Let X denotes the outcome of rolling a die.

a. Construct a graph of the (i) probability distribution of X and (ii) sampling distribution of the sample mean for n = 2. (You can think of (i) as the population distribution you would get if you could roll the dice an infinite number of times. The first column of Figure 7.8 portrays a case like this with the sampling distribution for n = 2. It shows also how the sampling distribution becomes more bells shaped as n increases to 5 and to 30.)

b. The probability distribution of X has mean 3.50 and standard deviation 1.71. Find the mean and standard deviation of the sampling distribution of the sample mean for (i) n = 2, (ii) n = 30. What is the effect of n on the sampling distribution?

a. Construct a graph of the (i) probability distribution of X and (ii) sampling distribution of the sample mean for n = 2. (You can think of (i) as the population distribution you would get if you could roll the dice an infinite number of times. The first column of Figure 7.8 portrays a case like this with the sampling distribution for n = 2. It shows also how the sampling distribution becomes more bells shaped as n increases to 5 and to 30.)

b. The probability distribution of X has mean 3.50 and standard deviation 1.71. Find the mean and standard deviation of the sampling distribution of the sample mean for (i) n = 2, (ii) n = 30. What is the effect of n on the sampling distribution?

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