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• The following questions are based on a distribution of scores w.pdf
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“There are bears in the area when blackberries are ripe.” What is the contrapositive of this statement? The converse? Solution In the classic structure: If P, then Q The contrapositive is defined by such: If NOT Q, the NOT P (because if P were the case, the original guarantees there would be Q, which we have said is not the case) The converse is defined by such: If Q, then P (just switch which thing you are saying is the antecedent (P) with the consequent (Q) in the if/then statement) So, for our case we have (re-arranging for the if/then format): IF blackberries are ripe, THEN there are bears in the area. Which fits the structure of IF P, THEN Q. So, P = blackberries are ripe, and Q = there are bears in the area So, applying the definition of the contrapositive (~Q => ~P): IF there are NO bears in the area, THEN blackberries are NOT ripe. And applying the definition of the converse (Q => P): IF there are bears in the area, THEN blackberries are ripe. Or, we can switch out of the classic structure into a more conventional structure. CONTRAPOSITIVE: When there are no bears in the area, blackberries are not ripe. CONVERSE: When there are bears in the area, blackberries are ripe. Hope that was clear enough, feel free to ask any clarifying questions. On a couple side notes, if the original statement is true, the contrapositive is definitely true because it is guaranteed by the logic. The converse MAY be true, but is not guaranteed by the original. If both the original statement and the converse are true, then it is a bi-conditional (i.e. P if and only if Q)..
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• The following questions are based on a distribution of scores w.pdf
- • The following questions are based on a distribution of scores with M = 75 and the SD = 6.38. • What is the probability of a score falling above a raw score of80? Solution Z = 80 - 75 / 3.68 = 5/8.68 = 1.35 P(z>1.35) = 0.088508