Consider the population of net gains for tickets in the California Decco lottery game described in Examples 1 and 2. The possible values are $4999, $49, $4, 0, and -$1; the mean is -$0.35, and the standard deviation is $29.67. Suppose that someone buys ten tickets each week.
a. Explain why the Central Limit Theorem would not hold for the distribution of possible mean net gains for the weekly purchases of ten tickets. In other words, explain why the sampling distribution of the sample mean is not approximately normal.
b. Although the possible means for samples of ten tickets are not approximately normal, you can still specify numerical values for the mean and standard deviation of the sampling distribution of the mean in this situation. What are they?
Example 1
The Long Run for the Decco Lottery Game In Chapter 8, we computed the expected value of the California Decco lottery game and found that the state gains an average of $0.35 for every dollar played. In other words, over all tickets sold, the state pays out an average of $0.65 and keeps $0.35.
Example 2
California Decco Losses In Chapter 8 and in Example 9.13 of this section, we discussed the California Decco lottery game, for which the mean amount players lose per ticket over millions of tickets sold is μ = $0.35.