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Unformatted text preview: a randomly selected married man and let W be the height
of a randomly selected married woman. Then M - W has a distribution that is
approximately normal with µ M −W = 70 − 65 = 5
σ M −W = σ M + σ W = 3 2 + 2.5 2 = 15.25 = 3.9051 Then P(M - W < 0) = P(Z < (0-5)/3.9051) = P(Z < -1.28) = .100 Part (b) is
Essentially correct if calculates the mean and standard deviation of M-W
(or W-M) correctly, and then correctly calculates the
appropriate probability. Partially correct if calculates the mean and/or standard deviation
incorrectly, but then uses these values and a correct process
to compute an appropriate probability
computes the mean and standard deviation correctly but is
unable to compute the appropriate probability. Copyright © 2000 College Entrance Examination Board and Educational Testing Service. All rights reserved.
AP is a registered trademark of the College Entrance Examination Board. AP® Statistics 2000 ─ Scoring Guidelines
c. Based on the answer to part (b), if heights of husbands and heights of wives were
independent, would expect approximately 10% of married couples to have the wife taller
than the husband. Based on the interval in part (a), the estimate of the percent of married
couples with the wife taller than the husband was between 3% and 7%. This is smaller
than what we would have expected to see if the heights of husbands and wives were
independent. So, the data suggests that heights of husbands and wives are not
independent. Part (c) is
Essentially correct if correctly judges independence (dependence) based on
responses in parts (a) and (b) and gives a good explanation
relating the probability in part (b) with the interval in part
(a). Partially correct if judgment of independence is consistent with the responses
in parts (a) and (b), but explanation is weak or poorly
linked to parts (a) and (b). Notes:
1. If the explanation compares the point estimate in (a) with the probability in (b), this is
considered a weak argument.
2. If explana...
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