For the following three questions, find some proportions (or areas under the curve). You need to become familiar with standardizing survey results by transforming them into Z (and later t) scores. Then, you have to find the probability of being to the left, right or between Z scores. The sign < means all the values (or area under the curve) to the left of the Z score. The sign > means all the values to the right of the Z score. For example, in standard z-score world, the probability that Z<0 = .50, or 50%. The probability that 0<Z<1 = .3413, or 34.13%.

Calculator from this week's forum or software (or drawing a picture often helps), find the proportion of observations from a standard Normal distribution (bell curve) for each of the following events, i.e., what proportion of the curve is in that area:

a) Probability that Z > 1.96

b) Probability that Z > 1.28 (or Z< -1.28)?

c) For some positive value of Z , the probability that a standard normal variable is between 0 and Z is 0.43735. What is the value of Z ?