1. What is the Central Limit Theorem? Try to state it in your own words. The Central Limit Theorem describes the characteristics of the "population of the means" which has been created from the means of an infinite number of random population samples of size (N), all of them drawn from a given "parent population". 2. What must be true so that the sampling distribution of distribution? What about the sampling distribution of x follows the normal p ? 3. Consider the random variable x, where x is a person's birth month (i.e., January=1, February=2, and so on). What is the (approximate) population distribution of birth month? What is the expected value of birth month? [Hint: You can ignore the fact that each month has a different number of days for the purposes of this exercise.] 4. Find the average birth month for students at your table. Is this variable normally distributed? Why or why not? 5. Find the average birth month for students in your class. (Your instructor will facilitate this.) Is this variable normally distributed? Why or why not? 6. Consider the random variable x , where x is the class average of birth month. What is the expected value of x ? What is the standard error of x ? [Hint: The population standard deviation of x is 3.45.] 7. What is the probability of obtaining a class average of birth month greater than the one you found in Question 5? 8. What is the probability of finding a class average of birth month within 0.5 months of the population mean? Make a sketch to illustrate the probability. 9. Suppose that your sample consisted of all students in Business Statistics. Would the probability you computed above increase or decrease? Why? 10. Now suppose you are interested in the proportion of students that have a fall birthday. What should this proportion be in the population? What is it for your class? 11. Find the standard error of the proportion. What is the probability of getting a sample proportion for fall birthdays less than what you observed for your class? 12. What is the probability of obtaining a sample proportion within 0.1 of the population proportion