1 . Generating the sampling distribution of the mean Suppose you use sampling techniques to estimate the mean of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. To do this, you perform an experiment in which you roll a twelve-sided die two times (or equivalently, roll two twelve-sided dice one time) and calculate the mean of your sample. The true mean () of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 is 6.5 , and the true standard deviation (o) is 3.45 There are 132 * possible different samples (of size 2) you could collect in your experiment, where different, in this case, means that rolling a 1 first and then a 5 is different than rolling a 5 first and then a 1. If you collected all of these possible samples, the mean of your sampling distribution of means (x ) would equal 6.5 , and the standard deviation of the sampling distribution of means (the standard error or or ) would be The following chart shows the sampling distribution of the mean (x ) for your experiment. Suppose you do this experiment once (that is, you roll the die two times). Use the chart to determine the probability that the mean of your two rolls is equal to the true mean, or P(x = p), is * . The probability that the mean of your two rolls is less than 11.5, or P(x