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Unformatted text preview: (10) 1. ‘\
\CA '2 For a certain list of incomes, the average income is higher than the median income.
All the incomes are positive numbers, and the units are dollars. Let x be the list. (a) Each income on the list is off the average income (average of x) by some amount.
True or false: r.m.s. of amounts off = I (av [X2] — (average of x)2 3 No explanation required. (b) Each income on the list is off the median income (median of x) by some amount.
True or false, and explain: _r.m.s. of amounts off =./ (av [x2] — (median of x)2 \ mm a a v as .5 \1 p (N. {Kw ‘, a” ‘ C‘.’ \‘G i; i 5 a a:
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‘w “ERAS kg’v’xfck guevw‘Q‘f . Tug W k Via} r J . 1. (continued) (c) For the list x:
r.m.s in (a) = $10,000
r.m.s in (b) = $10,440 (rounded to the nearest dollar)
For the list x, the average income is higher than the median income. By how much?
In other words, ﬁnd the difference: average of x — median of x. a; / {i 2“!) mvéxzy 2 W1“) "x W: if a ,i E {*1 ' w a
UAW r (wax. )~ TBgig/irz v ) K” Mw‘fﬁxi (10) 2. A small room contains 4 rows of 5 chairs: front of room 69 X ® . 69, X
x x x x x
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x x ,x. "X x back of room In (a), (b), (c) below, people enter the room one at a time, and the room is empty before
they start to come in. The ﬁrst person to enter is assigned at random to one of the twenty seats in the room; the second person to enter is assigned at random to the nineteen seats
remaining; and so on. ‘ (You can leave your answers in a box looking something like: Ans = 19 x (17/107 X 6/94 x 15/150 X 29/780 x 3/57) + + more terms like that Remember to show your reasoning, though.) (a) 'l\2vo people enter the room. Find the chance they end up sitting beside each other. at J: 7 r f .w' w ,
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r” ‘ 5" XFX/V’x/Vl “N” M ’5 (5) 3. A gambler playing roulette (in Nevada) can make a section bet—for example, bet $1 on
the numbers from 1 to 12 (inclusive). The bet pays 2 to 1: if one of the 12 numbers comes up, the gambler gets the $1 back, along with an additional $2. Otherwise, the gambler
loses the $1 stake. ’ A roulette wheel at Nevada has 38 slots, in each of which the ball is equally likely to fall.
The slots are numbered 0, 00, 1, 2, . . . 35, 36. Two gamblers, Ann and Bob, both like the section bet. Over a year Ann makes it 150 times
and Bob makes it 300 times. It might turn out that: (i) Ann wins more than 45 times.
(ii) Bob wins more 90 times. Check ( \f) one of the three options below, and then explain your choice. The explanation
should involve little or no calculation. (i) is more likely than (ii).
_, R X (i) and (ii) are equally likely. _ (i) is less likely than (ii). , r“
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:2” mantis if ﬂight? “at (if 6 atom: a? 19‘s? wisest? 2mm r s s (10) 4. The box below contains one hundred tickets, numbered from 1 to 100: HIE!!! Two hundred and ﬁfty draws will be made at random, with replacement, from the box. On any draw, the number on the ticket might be between 40 and 60 (inclusive).
Find, approximately, the chance this happens on 52 of the draws (no more, no les's). a ‘ .4 r , id ‘ U l taxman 1w M‘ f» ﬁlly“ m {"3 5W “I; $2} {:1 a f" big a ‘
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{I "I («‘0‘ (5) 5. In the presidential election of 1948, the error made by the Gallup poll in its prediction
of the popular vote was about 6 percentage points; in the election of 2004, it was 1.7
percentage points. True or false, and explain: The main reason for the better prediction in
2004 was that the Gallup organization used a much larger sample in 2004 than it did in 1948.
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all/Kl bmdc’ 7L airbag?“ 4W" whim “(Siig 3&3) j} (O . (10) 6. A survey organization takes a simple random sample of 500 residents from the Bay Area,
’ and asks everyone in the sample the following question: “Between now and 2025, California’s population is estimated to increase by 9
million people from 37 million to 46 million. On balance, do you think this popu
lation growth is a good thing or a bad thing, or does it make no difference to you and your family?”
To answer, please choose one of the four options below.
(i) a good thing (ii) a bad thing (iii) makes no difference (iv) don’t know. In the sample, 65 people chose (i); 280 chose (ii); 135 chose (iii); and 20 chose (iv). (a) Estimate the percent of residents in the Bay Area who think the population growth
described in the question is a goodcthing.“ ' — l a u!
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(c) The range from / O l/C’ to 6 /° is an approximate 95%conﬁdence interval
for the percent of residents in the Bay Area who think the population growth (describ
ed in the question) is a good thing. ( A .t O. a
l r! ., ,. ‘2: 5 l r" *“ ﬂ «(.7 1A “HA a [s Ur; :‘ é :; gm m, 2% ,Ma (Note: This problem is loosely based on a survey described in an article in the San Fran
cisco Chronicle of Thursday, January 5, 2006. The survey in the article was carried out by the Public Policy Institute of California. The numbers 65, 280, 135, 20 given in
problem 6 reﬂect accurately the ﬁndings of the real survey.) ...
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 Fall '08
 anderes
 Household income in the United States, The Gallup Organization, Bay Area, average income, George Gallup, median income

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