MATH 214 Midterm: MATH214_ALL-SECTIONS_FALL2009_0000_MID_SOL_1
10 Jan 2019
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Math 214 Fall 2009 Exam 2 Answer Key
1) The maple tree is in general the thickest. Maples had the highest median thickness. Half of the maple trees
were thicker than 3/4 of the cedar trees. Half of the maple trees were thicker than more than half of the pine
trees. The thinnest pine tree was thinner than the thinnest maple tree. The thickest maple tree was thicker than
the thickest cedar tree.
2a) voluntary sample 2b) simple random sample 2c) stratified sample
3) The voluntary sample (2a) is the most likely to be biased. A sample like this creates voluntary response bias,
where those who respond are more likely to be those with strong opinions.
4) TREE DIAGRAM:
Probability that both children are the same
gender = 8/20 or 40%
4b) Since the choice of child each night is
truly random, there is no way one can be
“due” for a night off. That kind of reasoning
is based on a “law of averages” that does not
exist. In the long run, Maynard can expect to
be chosen about 40% of the time. But short-
term behavior is inherently unpredictable in
random situations.
5a) S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18}
5b) S = {RB, RG, BB, BG, GG}
5c) S = {28, 30, 31}
6a) z = 1.15 ➝ .8749; 1 - .8749 = .1251;
12.5%
6b) z = -2.13 ➝ .0166; z = -0.49 ➝ .3121;
.3121 - .0166 = .2955; 29.6%
6c) top 15% ➝ z = 1.04; x = 59.344; round
up to 60 people
7a) .86 = .72 + . 55 - x; x = .41 7b) 1 - .86 = .14 7c) .41/.72 ≈ .57
7d) (.55)(.55)(.55)(.55) ≈ .09 7e) 1 - (.45)(.45)(.45)(.45) ≈ .96
8a) (8/15)(7/14)(6/13) = 8/65 ≈ .12
8b) sequence could be “odd-even-even” or “even-odd-even” or “even-even-odd”
(8/15)(7/14)(6/13) + (7/15)(8/14)(6/13) + (7/15)(6/14)(8/13) = 8/15 ≈ .37
Document Summary
Math 214 fall 2009 exam 2 answer key: the maple tree is in general the thickest. Half of the maple trees were thicker than 3/4 of the cedar trees. Half of the maple trees were thicker than more than half of the pine trees. The thinnest pine tree was thinner than the thinnest maple tree. The thickest maple tree was thicker than the thickest cedar tree. 2c) stratified sample: the voluntary sample (2a) is the most likely to be biased. A sample like this creates voluntary response bias, where those who respond are more likely to be those with strong opinions: tree diagram: Probability that both children are the same gender = 8/20 or 40% 4b) since the choice of child each night is truly random, there is no way one can be. That kind of reasoning is based on a law of averages that does not exist.
