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1. Find the probability value: (15 points = 5 points each) a) P(-0.32 g z 51.62)= b) P(z>-l.03)= c) P(zS-1.35)= 2. Find the value of zo, such that: a) P( -20 g z g 20) = 0.82 (5 points) b) P(z g 20) = 0.9082 (5 points) 3. The random variable X is normally distributed with mean 80 and standard deviation 12. a) What is the probability that a value of X chosen at random will be between 70 and 85? (10 points) b) What is the probability that a value of X chosen at random will be less than 75? (10 points) 4. The scores on a placement test have a moundshaped distribution with mean 400 and standard deviation 45. a) What percentage of people taking this exam will have scores of 390 or greater? (10 points) b) What percentage of the people taking this test will have scores between 415 and 435? (10 points) c) Mary is told that 90.82% of the students taking the test have higher scores than she does? What was Mary's score? (10 points) 5. A p_opulation of 40 year-old females has a mean salary of $39,321 with a standard deviation of $2,120. If a sample of 100 women is taken: a) What is the probability their mean salaries will be less than $38,000? (10 points) b) What is the probability their mean salaries will be between $38,500 and $39000? (10 points)