Discuss and explain the four rules for solving area-under-the-curve problems.
What will be an ideal response?
Ans: We can state the rules for solving area-under-the-curve problems very succinctly using the z-table. In all cases, we will assume a normal distribution with known mean and standard deviation. We will also assume that we’ve transformed scores to z-scores. Here are the rules:
Rule 1. The probability that a randomly chosen score will be less than z: P(z)
Rule 2. The probability that a randomly chosen score will be greater than z: 1 – P(z)
Rule 3. The probability that a randomly chosen score will be between z1 and z2 assuming z2 > z1: P(z2) – P(z1)
Rule 4. The probability that a randomly chosen score will be outside of the interval z1 to z2 assuming z2 > z1: 1 – [P(z2) – P(z1)]
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