For all these problems, it is not enough to simply state an answer; you must show your work in such a way that your reasoning is clear.
For section 6C: Do problems 18, 20, 32, 34, 40, and 42, as well as the following problem (a variation on the Martians-and-Venusians scenario discussed in class on April 25):
The land of Varia is divided into two equally populace provinces,
Lovaria and Hivaria. In each of the two provinces,
the average height of adult males is 5 ft. 8 inches.
However, in Lovaria the standard deviation is 2 inches,
while in Hivaria the standard deviation is 4 inches.
Assume that in each province, the distribution of
heights follows a normal distribution.
(a) Among those adult male inhabitants of Varia
who are 6 feet tall or taller,
what percentage come from Lovaria?
(b)
Among those adult male inhabitants of Varia
who are 6 feet 2 inches tall or taller,
what percentage come from Lovaria?
(c)
In light of what you (hopefully) learned
from parts (a) and (b),
explain why the following reasoning does or does not make sense:
"Although Africans constitute less than 50% of the world's population,
over half of the people over 7 feet tall are African;
therefore, Africans are taller on average than non-Africans."
(Leave aside the issue of whether the speaker's numerical assertions
--- "less than 50%", "over half" --- are correct,
and focus on the "therefore".)
For section 6D: Do problems 22, 28, 34, 36, 40, 42, 44, 46, and 48.
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