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**Unformatted text preview: **ARME 210 - I Name
Fall 2000 ID. Section MAKEUP PRELIM II
Please circle the Correct Answer. Each multiple choice question is worth 2 points. 1.) A discrete random variable: a.) cannot take on the values 1/8, 2/8, 3/8, and 5/8.
b.) cannot have negative values. c. cannot have the value zero.
(1. does not have probabilities greater then 0.01. x a does not give probabilities to intervals. 2.) A random variable is binomially distributed with mean 12 and
variance 8. Compute n. a.) 96 @ 36
b.) 40 .) 20 3.) Aperson with a Z-Score of -2.00 has performed below approximately
what percent of the students taking the test? a.) 2 percent (1.) 84 percent b.) 15 percent 97 percent
c.) 50 percent 4.) All of the following are characteristics of the normal distribution, except: ) symmetric about mean .) bell-shaped curve area under the curve is always one it is a discrete distribution .) probability that x is equal to any speciﬁc value is zero 900‘s» 5.) An instructor has ﬁve sections of a course: A, B, C, D, and E. She wants to
randomly select three sections for a special teaching evaluation. She labels the
classes as follows: A = 1, B = 2, C = 3, D=4 and E =5. She starts at the beginning
of this list of random digits: - 15689 14227 06565 14374
Which classes did she select?
a.) A, E, and A d.) B, C, and D
b.) AandD A7D,andE c.) A, B, and-C 6.) For work with the normal approximation to the binomial distribution, we
used a continuity correction because: .) the sample size was small.
.) the population variance was unknown. 0‘13? c the mean was estimated by n'p'
@ we were approximating a discrete distribution with a continuous
one.
e.) we were approximating a continuous distribution with a discrete
one. 7.) Which is NOT a characteristic of a (random) sampling distribution of
means? a.) Its mean is the same as the mean of the population
6D Its standard deviation is greater than that of the population
of scores. ‘
c ) It tends to resemble the normal distribution irrespective of the shape of the population of scores with sufﬁcient n.
d.) Its standard deviation changes with variation in sample size. 8.) As a rule of thumb, the sampling distribution of the sample proportions can be
approximated by a normal probability distribution whenever a.) up 2 5
b.) n(1 - p)? 5
c. n2 30 6, Both a and b are true.
e. None of the above answers is correct. 1o.) 11.) 12.) When the probability that an estimator is close to the parameter it estimates
increases as the sample size, :1, increases that estimator is said to be: The margin of error for a poll is 4%. This means that: a.) unbiased
b.) biased
c.) efﬁcient sufﬁcient
consistent a. 4% of those sampled did not answer the question asked we have 95% conﬁdence that the sample statistic is within 4% of the
population parameter 4% of those sampled gave the wrong answer to the question asked
4% of the population were in the sample f.) the conﬁdence we have in the statisticis 4%. Which of the following is a true statement regarding the comparison of
t-distributions to the standard normal distribution? a.) The normal distribution is symmetrical whereas the t-disttibutions
' are slightly skewed.
b.) The proportion of area beyond a speciﬁc value of t is less than the proportion of area beyond the corresponding value of z.
The greater the df, the more the t—disttibutions resemble the
standard normal distribution. All of the above.
e.) None of the above. In repeated constructions of 95% conﬁdence intervals for a
population mean, p, which of the following is most precise: a.) it falls in the interval approximately 95 times out of a 100.
the interval brackets the unknown u approximately 95 times out of a 100. c.) 95 out of a 100 populations will have their means in the
interval. (1.) Tt' falls in the interval approximately 95 times out of
a 100. e.) The interval brackets 7f approximately 95 times out of a 100. Please show your work and circle the correct answer. 13.) According to Runzheimer International, the average cost of a domestic trip for
business travelers in the ﬁnancial industry is $1250. Suppose another travel
industry research company takes a random sample of 22 business travelers in the
ﬁnancial industry and determines that the sample average cost of a domestic trip
is $1192, with a sample standard deviation of $279. Construct a 98% conﬁdence
interval for the population mean from these sample data. Assume that the data are
normally distributed in the population. Now go back and examine the $1250
ﬁgure published by Runzheimer International. Do you think that this value is
reasonable? Why or why not @ :l/q3,3:°?79 dFrQ/3 24.01;.025/g 2‘
(5) 07-7
#92 3: 3.5/9 [ﬁﬂ ﬂ
#9:? : N9. 75’ = («t/Ma 2:2, 1‘ /3I//. 78’) 9% c1 /
11 M50 sums reamab/e. 5712a nL falls (Ll/Mm W}, Jen/410 I
14.) You are planning to invest in a new high-tech company, and ﬁgure your rate of
return over the coming year as in the Table below (where 100% says that you
doubled your money, -- 50% says you lost half, etc.): - Rate of ,
Return Probability £5,615) 742 100% 0.20 ,20 0700 0
50% 0.40 a? 0 /0 0 0
0% 0.25 0 0
—50% 0.15 37 5
a.) Find the mean rate of return. 32' 5 33 7 5 (3) 1).) Find the standard deviation of the rate of return. ' 7
(4) 0‘ : 3375 v (32.52% = 337$?5 :
@ @ , c.) Find the probability that you will earn more than 40%, according to the
table. (a) P(x740%)== 15.) (6) 16.) (5) (6) A USA T oday/IntelliQuest survey of computer users revealed that 23% log onto
the Internet and/or an online service more than 20 times per month. Suppose a
random sample of 600 computer users is taken. What is the probability that more
than 25% of computer users log onto the Internet and/or an online service more
than 20 times per month? 7Z=éOO)/0=,g73 0 According to the Internal Revenue Service (IRS), the chances of your tax return
being audited are about 6 in 1,000 if your income is less than $50,000; 10in 1,000 if your income is between $50,000 and $99,999; and 49 in 1,000 if your income is
$100,000 or more (Statistical Abstract of the United States; 1995). a.) If ﬁve taxpayers with incomes under $50,000 are randomly selected, what
is the probability that more than one will be audited?
@ 72 = 5’) f = , 00 4 @
p m /) = /- [69600000994051‘ (,)(ao¢)’699¢)7 : /_ (gags! + .0393) x ,0003 G b.) If two taxpayers with incomes under $50,000 are randomly selected and two with incomes more than $100,000 are randomly selected, what is the
probability that none of these taxpayers will be audited by the IRS? 71:02,, f):,00¢) 1C(0)=:988 @
72:2, £5,049 ,rzo)-—.907/@ (988)6904) @ c.) What assumptions did you have to make in order to answer these Wail—“em? +MpaA/er5 audaled or 2207‘ Ind/award eve/(£8 ) and W25 W fro/3491 171/
OP be’bﬁ Qua/I Jed Kama/r75 Cmshuzzf 17.) According to Nielsen Media Research, the average number of hours of TV
viewing per household per week in the United States is 50.4 hours. Suppose the
standard deviation is 11.8 hours and a random sample of 42 US. households is take“ ,a=50.’/, a": //.f)72:€/2 a.) What is the probability that the sample average is less than 40 hours? If
the sample average actually is less than 40 hours, what could this mean in terms of the Nielsen Media Research ﬁgures? 22q0’5di4/:~57’2 , "‘8‘
=P(Z<—5.72)x0@ @ ¢roéany/u}s 2202‘ 50.s/Q (90 (6) b.) Suppose the population stande deviation is unknown. If71% of all
sample means are greater than 49 hours and the population mean is still
50.4 hours, what is the value of the population standard deviation. ‘4) -, 55 a 49—544
Q a/ﬁfz @ ~.55.-. -9,07 :7 J; /¢,s/9é
O“ 18.) According to ﬁgures released by the National Agricultural Statistics Service of
the US. Department of Agriculture, the US. production of wheat over the past 20
years has been approximately uniformly distributed. Suppose the mean production
over this period was 2.165 billion bushels. If the height of this distribution is .862
billion bushels, what are the values of a and b of this distribution? (6) I
grew-e “5:3 :7 5'4:- g: _. a‘l'b 171' [9.) Scores by women on the SAT-I test are normally distributed with a mean of 998
and a standard deviation of 202. Scores by women on the ACT test are normally
distributed with a mean of 20.9 and a standard deviation of 4.6. Assume that the
two tests use different scales to measure the same aptitude. If a woman gets an SAT score of 1220, ﬁnd her equivalent ACT score. :6) Z : /a’la?0—?QX ' 302 ' '
Q @ ‘r’lé 20.) According to Fortune (April 1994), proﬁts as a percentage of sales in the oil
industry during 1993 ranged from ——5% to 7%. If we wish to estimate average
proﬁts of sales with a 99% conﬁdence, what size sample should be drawn? Assume a margin of error of 2%. @ 0. 4, .7 _ f. g)
72’ (,:25'+*)°15’1 w v (6) 2 °‘ : M M 21.) A one-sided conﬁdence interval for p can be written as p < 1') +E or p > p —-E ,
where the margin of errorE is modiﬁed by replacing zcl ,2 with 20 . If Air America wants to report an on—time performance of at least x percent with 95%
conﬁdence, construct the appropriate one-sided conﬁdence interval and then ﬁnd
the percent in question. Assume that a simple random sample of 750 ﬂights ' results 1n 630 that are on time. ,7? z P ; 630 = I 8' 6/
$15G "H 0 @ ,M)@ 2,34,,031 ' ,8’7’ 11,545 750
0 22.) A US. Bureau of Labor Statistics survey showed that one in ﬁve people 16 years
of age or older volunteers some of hisor her time. If this ﬁgure holds for the
entire population and if a random sample of 200 people 16 years of age or older is
taken, what is the probability that more than 50 of those sampled do volunteer work? a
.— z - : 55:4
7Zm200)f .0? /u— 40,6 MIL @ é wagm P(x,v>5o,5) a Z:- 50. 'L/O z/tgvé 5.64
(8) [03/4 Q Bonus 23.) A 95% conﬁdence interval for the lives (in minutes) of Kodak AA batteries is
(430,470). Assume that this result is based on a sample of size 100. Construct
the 99% conﬁdence interval. @
1/50 I 97.57 00.4) 450 i 94 .2/ (443.79)4?4.2/) 99% CI/U
\/ Q‘) ...

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