Question: Suppose the probability is p = .2 that a person who purchases an instant lottery ticket wins money, and this probability holds for every ticket purchased. Consider different random samples of n = 64 purchased tickets. Let p^ = sample proportion of winning tickets in a sample of 64 tickets.
a. Give the numerical value of the mean of the sampling distribution of p^.
b. Calculate the standard deviation of the sampling distribution of p^.
c. Use the Empirical Rule to find values that fill in the blanks in the following sentence:
In about 68% of all randomly selected samples of n = 64 instant lottery tickets, the proportion of tickets that will be money winners will be between _ _ _ _ _ _ and _ _ _ _ _ _ .
d. Use the Empirical Rule to find values that fill in the blanks in the following sentence:
In about 95% of all randomly selected samples of n = 64 instant lottery tickets, the proportion of tickets that will be money winners will be between _ _ _ _ _ _ and _ _ _ _ _ _ .