## Question

# 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

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 *?

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### Fundamentals of Investments Valuation and Management

**Authors:** Bradford D. Jordan, Thomas W. Miller

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