Statistics-Probability hw

lloth 61
sl
Homework-
1
A. From handout 7.1, do problems 4,7,9, and 10.
B.
From hondout 7.2, do problems 2,4,6,8,!0,12.
C.
Do the
following problems.
L
The weights of the 45 plagers 0n 0 footboll teom are summarized in the
following frequencg distribution.
Weight
in nounds
l5l-
r75
I 76-200
201-225
226-250
251-275
276-500
Number
of nlauers
+
3
I
l5
12
7
2
a) Construct o histogram representing the dato.
b) Find the mean of the dota.
c) Find the variance and stondard deviation of the data.
2.
Find the mean and the median
aJZ4681012
bl 2 4 6 B t0 t20
for the given raw data:
c) How do gour answers for a) and b) differ (or agree)? Whg?
3. Find the variance and standard devistion
o)i 6 I 12 15
b) 13 16 r9 22 2s
c) 3O 60 90 120 150
for the qiven raw data:
d) The data in b) was obtained bg adding I 0 to each of the pieces of data in
a) nnd the doto in c) was obtained bg multiplging the dota in a) bg 10.
How do the corresponding variances and standord deviations compare?
PROBLEM SET 7.1
L An ordinary die is tossed. What
is the probability that the number
of spots on the upper lace will be
(a) Three? (b) Greater than 3? (c) Less than 3?
(d) An even number? (e) An odd number?
2. Nine bails. nrrmbered l, 2, . . . , 9, are in a bag. If one is drawn at
randorn, rr'hat is the probability rhar its number is
Nine? (b) Cireater than 5? (c) Less than
(a)
recorcl lhe outconres by listing the numerals on the bottom faces,
(a) Horv man,v outcomes are there?
(b) What is the probability of a sum of 7?
(c) What is the probabi.lity of a sum less than 7?
s. What is rvrong with each ol the following statements?
(a) Since there are 50 states, the probability of being born in
Wyoming is $.
(b) The probability thaI a person smokes is .45, and that he drinks,
.54; rhere{bre the probability that he smokes or drinks is.54 *.45
l,""0
11.
6?
(d) Evcn? (e) Odd?
3. A penrrt,:r nickel, and a dinre are tossed. List the eight possible
outcomes of this experiment. Whar is the probability ol
(a) Three heads? (b) Exactly two headsT
(c) l\lorc tlrirrr orrc hcad?
f(L'l q A c<;in ancl a die are tossed. Suppose that one side of the coin has a
I on it, and the other a 2. List the l2 possible outcomes o[ this
experiment, e.g., (1, l), (1,2), (1,3). What is the probability of
(a) A total of'4? (b) An even total? (c) An odd total?
5. T*'o ordinarl dice are tossed. What is the probability of
(a) A double (borh showing the same number)?
(b) The ntrnrbel on one of the dice being twice that on the other?
(c) Tlre nurlbers on the trvo dice differing by at least 2?
6, A letter is choserr at randonr from the word PROBABILITY. What
is thc probability that it will be (treating Y as a vowel)
(c) M? (d) A vowel?
(a) P? (b) B?
kt'vl . Two reguiar tetrahedra (tetrahedra have four identical equilateral
triangles lor faces) have their faces numbered l, 2, 3, and 4.
Suppose they are tossed and we keep track of the outcorrie by listing
rhe numerals on the bottom faces, e.g., (1, l), (1,2).
(a) How many outcomes are there?
(b) What is the probability of a sum of 7?
(c) What is the probability of a sum less than 7?
8. Two regular octahedra (polyhedra having eight identical faces) have
their laces numbered l,2, . .. ,8. Suppose they are tossed and we
(1,)
rlhat is the probability rhar a studenr w
registers next year
(a) Will get an A or a B?
(b) Will not get either an A or a B?
A poll was uken at Podunk University on rhe question of coeducational dormitories, producing the follorr'ing results.
class. Based on these data,
= .9!
(c) The probability that a certain candidate for president of the
Uniterl States will win is *, and that she will lose, *.
(d) lwo lootball teams A and B are evenly matched; therelore the
probability that A will win is *.
During the past 30 years, Professor Witquick has given only 100 A's
anrr tpB's in Math l3 to the 1200 students who registered for the
TABLE 7.1
Admlnlstrators
Fsculty
Studonts
Tota
120
300
For
4
16
Against
3
32
No opinion
3
2
100
100
40
Tornl
10
50
240
45
On the basis of this poll, rvhat is the probability that
(a) A randomly chosen faculty member will lavor coed dorms?
(b) A randomly chosen student rr,ill be againsr coed dorms?
(c) A person selected at random at Podunk University will favor
co
dorms?
(d) A person selected at random at Podunk Universiry will be a
faculty member who is against coed dorms?
12. The well-balanced spinner shown at the left is spun. What is rhe
probability that the pointer h,ill stop at
(a) Red?
(b) Green?
(c) Red or green?
(d) Not green?
13. Four balls numbered l, 2, 3, and 4 are placed in a bag, rnixed, an
drawn out, one at a time. What is the probability that they will be
drawn in the order l, 2, 3, 4?
14. A five-volume set of books is placed on a shell at random. What is
the probability they will be in the right order?
15. From an ordinary deck o[ 52 cards, I card is drawn. What is the
probability that it will be
(a) Red? (b) A spade? (c) An ace?
Note: Two ol the suits are red, and trr'o are black.
16. From an ordinary deck of cards, two cards are drawn. This can br
done in rrCr wa),s. Whar is the probabilitt'that both rvill be
(a) Red? (b) Ol the sarne color? (c) Aces?
17. From an ordinary deck of 52 cards,3 cards are drawn. What is th
probability that
(a) All will be red? (b) All will be diamonds?
(c) Exactly I will be a queen? (d) All will be queens?
18. If three men and two rvomen are seated at random in a row, what
the probability that
(a) Men and women will alternate?
(b) The men will be together?
(c) The women will be together?
PROBLEM SET 7.2
l.
/":1-x
44
6F\
\:jy W
I
-I-oss
a balanrc<l die thrcc times in sttccessittn. \\'h:rt is thc probabilitv of all I's?
[4u2. -f,r., a [air coin [<rtrr timcs in srrccessiott. \\'hat is thc probabilitr of
all heads?
11 Spin 1[s 1*o slrinncrs picturcd at thc lcfi. \Vhat is the probabilirv
that
(a) R<rth uill shon re<l?
(b) Neithcr xill sh<'u rc<l?
(c) Spinrrer A rr'ill sh<ls retl :rnd sPittttcr Il rtttt rerl.'
| "{
h"W
(d) Spinncr A will shorv rcrl anrl spinrtcr l] rc<l ,rr (recn?
(e ) ust one oI the spinncrs rvill shorn' grectt:
J
The two bxrxes shown belor^'are thoroughll'shakcn and a ball
drawn lrom each. What is ttre probabilitv that
(a) Both will be I's?
(b) Exactlv orrr of thenr u'ill bc :r 2?'
(< ) Both will b<' t'r'err?
(tl) Exacth onc o{ thent rr'ill t>c cvcrr:
(c) .{t
le:rst orrc
ol thcltt rvill bc t'r't
tri'
An urn cotttains five rccl balls arrd scvert blltck balls. l'rttt balls are
drawn in strccessiorr. Wlrlt is tltc lrrrrbabilitv o{'drart'irrg two rcd
balls if'
(a) The first b:rll is replacc<l betirre tltc sc<otrtl is <lraun?
(b) The first llall is ttot relrlatcrl belirre tlte sc<-ott<l is <lrawrr?
bWU O. Answcr thc rlrrestiorrs in llrohlcnr 5 il thc ur.n <.onr:rirrs {ivg y",1
balls. six bla< k b:rlls. arr<l scr.crr gr.ccrr ll:rll.s.
7. (iiven that /'{.1} :.tt. I,(tll :.i.:rnd t,(.t n /J} =..1. firr<l
(a) /'(.{ U /l)
(b) /,( /J | .r )
(() /'(.Jl/,)
(iiven that I'(..11 : .tl. l,(lt ) : .{. :rnd I,(8l.|: .tt. fincl
8.
W*j
(a) I'(.-l fl ll)
(b) /,(.I u l|
((\ I'1. lllt )
9. In ea<:h casc irt<lir';r(e whether.ot. rrot thc tw() cven(s seem indc_
pendent to v()r.1. Expllin.
(a) (ietring an A in phvsir:s and gerting arr A in math.
(b) Getrirrg arr A in phlsi<:s arrd winnitrg thc rennis nrarch.
(c) (ictting:r .crv shirr f.r v..r rrirthdav arr<r stubbi.g \.()ur t()e
the next dar'.
(cl) Going to H:rrr.:rrd and bcing an Americarr Indiarr.
(e) Being :l \{ontan arrd bcirrg .r d(x:t()r.
1fl Walkinu ttttder
a l:rddcr':tttd h;rsinq un ur:r'iden( rhc rrexr rlar'.
irrdi<:arc rvhctlrcr.(hc rrro evcnts ar.c clisjoirrr.
(;r) ()crring an.{ in l)hr.sit.s l{) l arrrl qerrirrg a Il in phlsirs l0l_
1b) l-he strrr shininrr on l'rresd:rr.:rn<l rairrirrg orr Trrcsdar.
(r') ln tossing tu,o dice. gcttintl:rrr o<lrl srrrrr:rntl gcrrinu rhc sanrc
irt.*.t ,,, Irr each tasc
number
or-r
each die.
(d) ln tossing trro dice, getring:rrr odd sunr lrrd gerring a six on
one of rhe dice.
1e) Gerring an
(f)
A in
1>hrsics
and getting arr
,\ in rnath.
Not losing the football garne arrd no( \\'innin{ rhc lootball qanrc.
ll. A nlaclrirtc pt<lduces boits rrhiclr aic l)ul in b,rxes. It is kntirrrr thut
I box in l0 rvill har.e ar lcasr onc defccrive bolr in ir. _\ssunring
IJ
tv
that the boxes are irrclepertdent of eac:lr tirher. rthat is rlre probabilitr
that a cusronrer who ordered iJ boxes rrill ger all go<td bolrs-:
I2. Suppose the pr<lbabilirv oI being hospiralized during a vear is .20.
Assuming indel>ende'ce of familr nrenrbers, rr.har is rhe pr.babilir'
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