Questions
on Topic Eleven:
The Normal
Distribution
2
Questions on Topic Eleven:
The Normal Distribution
Itiple-Choice Questions
I.~
.
~"Which cif the following is a true statement?
:,@)The
area undet a notmal curve is :alwa;s equ~l col, nomalte; wh~t the
. mean and standard deviation are.
. .... ".
.... . .
(B) All bell-shaped curves are normal distributions for some choice of
Il and cr.
(C) The smaller the standard deviation of a normal curve, the lower and
. more spread out the gtaph.
(D) Depending upon the value of ~hestandard deviation, normal curves
• with different means may be centered arounq the s~me number:'
(E) Depending upon the value of the standard deviation, the mean and
median of a' particular normal distribution may be different ..
Which of the following is a.t~ue statement?
(A) The area under the standard normal curve between 0 and 2 is'twice the
1.
'.
~The
area under the standard normal curve between 0 and 2 is half the
' .. area between ~2'and 2,> .' '.
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(C) FOr the standard normal curve, the interquartile range is approximately 3.
(D) For the standard normal curve, rhe range is 6.
(E) For rhe standard normal curve, the area CO the left of D.l is the same as :/:..
. the area to the right of 0.9, ~
.
__'\ ~ - SCQrC-~
£\ area betWeen 0 and
Populatr~ns PI and P2 are normally distributed and have identical means.
Howev!r, the standard deviation of PI is twice the standard deviation of P2..
Wh.at can be said about t.he percenr;;g;; of observatio.ns falling wlthin tw~.
standard deviations of th,e mean for each population?
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(A) The percentage for P I is twice the percentage for P2.
(B) Tile percentage for PI is greater, but not twice asgreat, as the percentage for P2.
.
(C) The percentage for P2is twice the percentage for PI.
.
(D) The percentage for P2 is greater, but not twice as great, as the ~ t1r \?(L.--h(M..)
~
percentagefor Pl...
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~The
percentages are identical.
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278
AP Statistics
4. Consider rhe following two normal curves:
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b
a
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15
10
.5
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25
20
Which has rhe larger mean and which has the larger standard deviation?
(A)
(B)
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(E)
Larger mean,
Larger mean,
Larger mean,
Larger mean,
Larger mean,
larger standard
a; larger standard
b; larger standard
b; larger standard
b; same standard
deviation,
deviation,
deviation,
deviation,
deviation
a;
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b
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b
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In Questions 5-15, assume rhe given distributions are normal.:'
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5. A trucking firm derermines that irs fleer of trucks averages a mean of 12.4
miles per gallon with a srandard deviarion of 1.2 miles per gallon on cross-';~
.,,~.
country hauls. What is (he probability that one of rhe trucks averages fewer}~
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(C)
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than 10 miles per gallon?
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(0) .5228
11
(E) .9772
6. A factory dumps an average of 2.43 tons of pollutanrs into a river every wee~'!
If rhe srandard deviation is 0.88 tons, what is the probability that in a week~1
more rhan 3 tons are dumped?'
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(B) .2843
.' (C) .6500
-4. (D). 71 57
(E) .7422
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7. An electronic product takes an average of 3.4 hours to move through an ',;(illl
assembly line. If the srandard deviarion is 0.5 hour, what is rhe probability;~1
thar an item will take between'S and 4l\ours?
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(A) .2119;~
(B) .2295
(C) .3270
D.3811
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Ol)estions on Topic Eleven: The Normal Distribution
279
vemeanscore on, ~c()ll~geplacement exam is 500 wirh a srandard devia"pn'of 100.Ninety-fivepercenr'of the test takers scote a~ove what?
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J1e:,-veragenoise level in a restautant is 30 decibels with a standatd devlai,Jp.of4 deCibels,Ninety-nine percent of the time it is belpw what value?
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,h~ ~ean in~ome per household in a cerrai'n stare is $9500 with a standat~
• eviation of $1750, The middle 95% of incomes are between what'two
allies? '
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$5422~n'd$13,578
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6b7i)~nd'$12,930
c::)$6621 a~d.$12\379,
(D) $7260and $11,740 '
~E) $8049 and$liJ,951
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i'JayOlsh~nsky f?tm the Univetsity of Chicago was quoted in Cha"/teN~wsas
Jatgliing rhat for tbe~ve~ageJife expectancy wreachlO.o,)8O/o of people'
.
. wouldha~eto Iive.roJ20.W!lat, standarddeyiationishe
asiurping,f{)tthis'
.; statement to makeosense? '. ,': '." ' "
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One company produces movie ttailerswith mean '150 setbrids' and standatd
deviation 40 seconds, while a second company produces trailers with m~n
'i20s~condsand standard deviation 30 seconds. Whatisthe pro'babilirythat
,tworandomly selected nailers, ()neptoduced by ,each co~pany,' will combine
. to less th~nthreeininutes?'.
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13. Cucumbers' grown on a certain farm have weights with a standard deviation.A
~f 2 ounces ..What is the mean weighr ifJ!29'o of the cucumbers weigh iess'~
than 16 ounces?
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B) 14.30
(C) 14.40
(E) 15.70
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(B),u = 56.26,0' = 11.85
~,u = 118.52,0' = 56.26
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16. Assume that a baseball team has ar: average pitcher, that is, one whose pro~
bility of winning any decision i~. If this pitcher has 30 decisions in a se~i
son, what is the pro.bability that he will win at least 20 gam,s?
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(E) ,u= 139.45,0' = 83.33
~6.97
ounces
(B) 7.22 ounces
(C) 7.34 ounces
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15. A coffee machine can be adjusted to deliver any fixed nu~ber of ounces o(i
coffee. If the machine has a standard deviation in delivery equal to 0.4 oun"
what should be the mean setting so rhat an 8-ounce cup will overflow only;'
05% of the time?
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14. If 75% of all' families spend more than $75 weekly for food, while 15%
.
spe~.d~ore
than $150, w~at is the mean weekly{expe diture and what is th...~'¥I
stanaard deviation?
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(0) 14.88
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(B) .2514
(C) .2743
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(E) .•4300 .
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17. Given that 10oP:f the nails made using a certain manufactuting process
a length lessthan 2.48 inches, while 5% have a length greater than 2,54
inches, what are the mean and standard deviation of the lengths of the
~me
that the lengths havea normal distribution.
W,u = 2.506~~
(B) ,u'= 2.506, 0' = 0.0410
(C) ,u = 2.516, 0' = 0.0825
(0) [J. = 2.516, 0' =0.1653
(E) The mean and standard deviation cannot be computed from the info'
mation given.
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