Two balanced dice are thrown, and the average number on the two upper faces is recorded.

a. Use the values μ = 3.5 and σ = 1.71 from Exercise 7.84. What are the theoretical mean and standard deviation of the sampling distribution for x
?

b. Use the Central Limit Theorem applet to toss a single die at least 2000 times. (Your simulation can be done quickly by using the button.) What are the mean and standard deviation of these 2000 observations? What is the shape of the histogram?

c. Compare the results of part b to the actual probability distribution shown in Figure 7.4 and the actual mean and standard deviation in part a.