For Problems 9 - 12: A certain breed of cattle has weights that are normally distributed with a mean of 1650 pounds and a standard deviation of 75 pounds.

9. If one cow is selected at random, find the probability that its weight will be 1600 pounds or less.

10. If one cow is selected at random, find the probability that its weight will be between 1600 and 1680 pounds. [Hint: You're dealing with a band of area in the middle of the normal bell curve.]

11. What weight(to the nearest pound) represents the 67^th percentile in this group of cows? [Hint: Find the z-score corresponding to a probability of 0.6700 and substitute it into the z-score formula. Then algebraically solve for x which will be the desired weight at the 67^th percentile.]

12. (10 pts) If a group of 9 cows is selected at random, find the probability(to nearest 0.0001) that the mean weight of the group will be 1600 pounds or less. [Hint: Compared to Problem # 9 dealing with only one cow, it is intuitively harder to select a group of 9 cows that have a mean weight of 1600 pounds or less given that the mean weight of the breed is 1650 pounds. This calls for a revised standard deviation for the group that will result in a higher z-score and a lower probability for this situation.]