A red die and a blue die are rolled. You win or lose money depending on the sum of the values of the two dice. If the sum is 3, 8, or 9, you win $6. If the sum is 10 or 12, you win $2. If the sum is any other value (2, 4, 5, 6, 7, or 11), you lose $3. Let X be a random variable that corresponds to your net winnings in dollars. What is the expected value of X?

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? why? a. the z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. b. the z score of 0 is most preferable because it corresponds to a test score equal to the mean. c. the z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. d. the z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average