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2.9 During the instruction period referred to in lowing are the grades made by the members of the group: 73 65 82 70 45 50 70 54 32 75
75 67 65 60 75 87 83 40 72 64
58 75 89 70 73 55 61 78 89 93
43 51 59 38 65 71 75 85 65 85
49 97 55 60 76 75 69 35 45 63 (a) Group these grades into a di
50—59, . . . , and 90-99. (b) Convert the distribution of part (a) into a percentage distribution. stribution having the classes 30—39, 40—49, . as
u 1‘ a.” ..
‘0 u ' ' i ’ bin 'obs in one city turned
t‘ 18 éwl ompleted home plum ‘ g 1 . _
3.10 angnipgcgog % l, 0‘: 4, (ii, 5.1, 1, 2,. 0l 1, 0, and 2 violations of the city build- in code. Find
(a)g the mean; (c) the mode.
(b) the median; 5.1 A person with $2 in his pocket bets $1, even money, on the ﬂip of a coin, and he continues to bet $1 so long as he has any money. Draw a tree diagram to show
the various things that can happen during the ﬁrst threeﬂips ot' the coin. In how many of the cases will he be (it) exactly $1 ahead; (b) exactly 81 behind? ' , 5.6 A woman can buy
of ﬁve colors. How many choices does she have? 5.13 A true—false test consists of 15 questions. In how many ways can a stude'nt
mark her answers to these questions? 5.8 It“ the NCAA has applicatiOns from {our universities for hosting its inter-
collegiate swimming championships in 1984 and 1985, in how many ways can
it select the sites for these championship meets
(a) it' they are not to: be held at the same university; (b), if they may be held at the same university? 5.24 Calculate the number of ways in which a discount chain can choose 2 of 12
locations for the construction of new stores. . 5.38 If two different cards are drawn from a well-shufﬂed deck of 52 playing cards,
what are the probabilities of getting - 811)) two hearts; (c) a‘king and a queen?
two aces; the preceding exercise, the study
group was given a test on number systems and Boolean algebra, and the f0]- .7 Erma 'Paoeusns covey-(J '\'v'\ V {Jukni-Ixes
P.‘ 09 Z 6.19 With reference to the preceding exercise and the Venn diagram of Figure 6.6,
express in words what events are represented by the following regions: (a) region 1; ((1) regions 3 and 5 together;
(b) region 5; (e) regions 1 and 4 together;
(c) region 8; (f) regions 6 and 8 together. 6.25 1! Fund Tare the events that a one car owner in a certai
drive a Ford or a Toyota, and abilities that such a person will
(a) not drive a Ford; (b) drive a Ford or a Toyota;
(c) drive neither a Ford nor a Toyota. n income bracket will
HF) = 0.34 and P0) = 0.08, ﬁnd the prob 6.65, Among the 80 pieces of luggage loaded on a plane in San Francisco, 55 are
destined for Seattle and 25 for Vancouver. if two of the pieces of luggage are ..sent to i’ortland by mistake and the “selection" is random, what are the
probabilities that ' ' (a) _ both should have gone to Seattle;
(b) both should have gone to Vancouver;
(c) one should have gone to Seattle and one to Vancouver? 9|. 8.1 In each case determine whether the given values can be looked upon as the values of a probability distribution of a random variable which can take on
only the values 1, 2, 3. and 4, and explain your answers: (a) f(1) = 0.24, [(2) = 0.24, f(3) = 0.24, f(4) = 0.24; (b) f0) = l. f(2) = %.f(3) = 42'. f(4) '= %: (c) f(1) = 0.15, f(2) = 0.38, f(3) = 0.24, [(4) = 0.23;
(d) f(1) = 0.23, f(2) = 0.42, f(3) = —0.03, [(4) = 0.38; (e) m) = l. f(2) = 3. 1(3) = 1.. f(4) = 11.. - I 8.7 In the game of f‘chuck-a-luck" three dice are thrown and a player bets on the . occurrence of a number which he can choose. If he wins 8 i if his number appears on only one die, 52 if his number appears on two dice, $3 if his number appears on all three dice, and he loses 51 if his number appears on none of the dice, ﬁnd the probabilities of his inning $1, $2, $3, and the probability of his losing 31..
Also determine the player's mathematical expectation. i
8.8 A bank knows that 60 percent of its checking-account customers will pay extra
for personalized cheeks. Find the probability that at most two of eight ran- domly selected checking-account customers will pay extra for personalized
checks. 8.26 It is known from experience that 2.8 percent of the calls received at a company
switchboard are wrong numbers. Use the Poisson approximation to the
binomial distribution to determine the probability that among 250 calls
received at the switchboard, 6 are wrong numbers. 8.28 If 'the number of complaints which a laundry receives per day is a random
variable hating the Poisson distribution with 1. = 3.5, ﬁnd the probabilities
that on any given day the laundry will receive
(a) no complaints; (c) two complaints; (b) at least one complaint; (d) four complaints. 9.6 In a cannery, production lines I, II, and III account for 50, 40, and 10 percent
of the total output. If 0.5 percent of the cans from line I, 0.6 percent from line
II, and 1.5 percent from line III have faulty seals, what are the probabilities
that a can with a faulty seal, detected at ﬁnal product inspection, was produced
by
(a) line I; (b) line II; (c) line III? 12.4 The management of a resta'urant found on the basis of a random sample of
size n =1 50 that it took its head chef on the average 52 = 14.7 minutes to pre-
pare a particular cooked-to-order entree; the standard deviation of the sample
is s = 4.8 minutes. What can we assert with 98 “A conﬁdence about the possible
size of the error in the estimate 55 = 14.7 minutes of the true average time it
takes the chef to prepare this item? 9.26:2— 12.11 It is desired to estimate the mean lifetime of a certain kind of electronic com-
ponent. Given that a' = 65 days, how large a sample is needed to be able to
assert with probability 0.95 that the estimate will be off by at most 20 days? 12.25 Suppose that in the ﬁlling example the criterion is changed so that the hypothe- sis p = 300 grams is accepted if the sample mean falls between 298 and 302
grams; otherwise, the hypothesis is rejected. ' ' (a) Show that this will increase the probability of a Type I error from 0.0026
to 0.0456. (b) Show that this will decrease the probability of a Type II error when ,1: =3 '
296 from 0.1587 to 0.0228. 12.34 The security department of a factory wants to know whether the true average
time required by the night watchman to walk his round is 30 minutes. If, in a
random sample of 45 rounds, the night watchman averaged 29.2 minutes with
a' standard deviation of 1.6 minutes, determine at the level of signiﬁcance 0.05
whether this is suﬁicient evidence to reject the null hypothesis [1 = 30 minutes. 12.35 In trying to rent a location for a restaurant in a shopping mail, a rental agent
assures a restaurant owner that on an average business day at least 3,600
persons pass through the mall. Being a cautious businessman, the restaurant
owner hires a ﬁrm to conduct a survey, and this survey shows that on the
average 3,453 persons, with .a standard deviation of 428 persons, passed
through the mall on 32 randomly selected days. Use the 0.05 level of signiﬁ- cance to test the null hypothesis ﬂ = 3,600 against the alternative hypothesis
[l < 3,600. 12.39 The police chief of a large city claims that the mean age of bicycle thieves is
9.5 years. A research worker who feels that this ﬁgure is too low takes a
random sample of 80 cases of bicycle theft from police ﬁles, and ﬁnds the mean
age of the thieves to be l0.8 years with a standard deviation of 4.3 years. What can the research worker conclude from these ﬁgures at the level of signiﬁcance
at = 0.0l ? . \ - LL ...

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- Spring '11
- Moondra
- Statistics