A common technique in the field of testing is to design the test so that it will have a mean of 50 and a standard deviation of 10. Examples are the MMPI (Minnesota Multiphasic Personality Inventory), CPI (California Personality Inventory), and the Tennessee Self-Concept Scale. (Perhaps when you become a famous test maker, you'll name your test after your school.)

Please show work and be sure to identify the associated Z scores as well as the p value so that you can earn as many points as possible. a. From a thousand persons (n=1000) how many would be expected to get a clinical label, which is 2 standard deviation from the mean? b. What proportion would be expected to score 68 and above? c. What proportion would be expected to score between 53 and 63? d. What score separates out the lowest 20%? e. If there were 150 patients, how many is anticipated to score 65 or above?

f. What proportion is expected to score 18 or less?