1. Can SS ever have a value less than zero? Explain your answer. (2 points)
2. Researchers comparing the cognitive skills for younger adults and older adults typically find greater differences (diversity) in the older adults. Following are typical data showing problem-solving scores for two groups (samples) of participants. (8 points)

OLDER ADULTS: 19, 4, 7, 13, 8, 6, 1, 9, 12, 3, 10, 2, 3, 1, and 18

YOUNGER ADULTS: 7, 9, 6, 6, 8, 5, 5, 4, 6, 6, 7, 9, 9, 5, and 6

1. Compute the mean, the range, the variance and the standard deviation for each group.
2. Is one group of scores more variable than the other?
3. In a population distribution, a score of X = 38 corresponds to a z = -2.00 and a score of 104 corresponds to a z = 10. Find the mean and the standard deviation for the population. (3 points)
4. A distribution with a mean of 76 and a standard deviation of 8 is transformed into a standardized distribution with a mean of 90 and a standard deviation of 17. Find the new standardized score for each of the values from the original population. (8 points)
   1. X = 63
   2. X = 72
   3. X = 100
   4. X = 105
5. Find the z-score boundaries that separate a normal distribution as described in each of the following. (4 points)
   1. The middle 32% from the 68% in the tails.
   2. The middle 80% from the 20% in the tails.
6. S.M.A.R.T. test scores are standardized to produce a normal distribution with a mean of 240 and a standard deviation of 20. Find the proportion of the population in each of the following S.M.A.R.T. categories. (6 points)
   1. Genius: Score of greater than 290.
   2. Superior intelligence: Score between 255 and 290.
   3. Average intelligence: Score between 223 and 255.
7. Name and describe a profession where understanding how to calculate and understand probability is crucial. Explain why you think this and give a specific example form their job where it would be important and what would happen (the negative consequences) if they didn't. NOTE: Using sources/references to support your answer is important for this question. (20 points)