Refer to the die-tossing experiment with n = 1 in Section 7.4 in which x is the number on the upper face of a single balanced die.

a. Use the formulas in Section 4.8 to verify that μ = 3.5 and σ = 1.71 for this population.

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 7.3 and the actual mean and standard deviation in part a. They should be similar!