ALL of the following questions, show all your calculations and as far as possible, round off/up to two decimal places. 1. The following data set indicates the scores obtained by a sample of 12 participants on a self-esteem measure. Compute the variance for the following data. (4marks) 136 127 165 159 142 141 152 139 142 157 161 170 2. Compute SS for the following population and then find the population variance and the Standard deviation. Scores: 7, 2, 0, 6, 8, 6. ( 7 marks) 3. We wish to standardise a distribution which currently has a population mean of = 45 and a standard deviation of = 7 to one where the population mean is = 100 and the standard deviation is = 20. If a subject obtained a score of x = 42 on the current distribution, what will his/her score be on the new distribution? (4 marks) 4. A sample of n = 16 scores is selected from a normal population with = 60 and = 20.(8 marks) a. What is the probability that the sample mean will be greater than 50? b. What is the probability that the sample mean will be less than 56? 5. A normal distribution of scores has a variance of 2=100. Find the z-scores corresponding to each of the following values: (10 Marks) a. A score that is 20 points above the mean. b. A score that is 10 points below the mean. c. A score that is 15 points above the mean d. A score that is 30 points below the mean. e. A score that is 5 points above the mean. 6. For a sample with M = 38 and = 12, find the X value that corresponds to each of the following z-scores: -0.25, -1.50, 0.50, 2.00 (8 marks) 7. For a normal distribution with a mean of = 100 and a standard deviation of = 10, find each of the following probabilities: (10 marks) a. p(X > 107) b. p(X < 75) c. p(X < 120) d. p(95 < X < 105)