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Unformatted text preview: NAME STUDENT NUMBER
STA22OH5F L0101 University of Toronto Mississauga November 11, 2009
TERM TEST II Duration 50 minutes
AIDS PERMITTED: Calculators, one 8.5 by 11" aid sheet Statistical tables will be provided. The marks on this test add up to 50.
(10 Marks)
I. If the statement is true circle T otherwise circle F.
A. The mean of the standard normal distribution is 0. @ F
Bl The mean of the Poisson distribution equals its median. T ®
C. The normal approximation can not be used for some hinomials. T F
D. The conﬁdence level for a 90% Conﬁdence Interval is 90%. F
E. The sampling distribution of medians is approximately normal. T Q
F. The width of a conﬁdence interval equals >’< t SE, T ©
G. The sample standard deviation s is a parameter. T (F)
H. We should correct for continuity when we compute the probability in
the normal distribution, T @
I. If 52 = (72 then s2 is an biased estimator of oz. T @
I. If we increase the sample size n then the Width of the conﬁdence
interval decreases. F [10 marks] H. A telephone company knows that long distance telephone bills are normally distributed.
A random sample of 40 customers is selected and the mean bill is $25 with a standard
deviation is $10. A. Give a 90% conﬁdence interval for u. 95’: {Meow/v16
agaicjo @ £12.40 a 7.690 B. Suppose the company wants to estimate the mean within $2 with 95 % conﬁdence
How large a sample is required? x ‘ %\
n :Wt hall: W74 11 C” Page 1 of 3 C. The company gets another sample of 20 and the mean is $20 with a standard
deviation of $10. Find a 99% conﬁdence interval for p. tookﬂjq> :_ g“ ,QQ, ’ 950::9m8t7l003/WT5
iédo 6E
Lita) M0 (10 marks)
HI. Pulse rates for adults have a normal distribution with a mean of 70 beats per minute and
a standard deviation of 15.
A. What proportion of the population has pulse rates of less than 73? 7 "s a T 0
T? (a < :CP 0 . 1,1 0 :
‘5 C?“ > (0. s7 93 0 . s” + . o 7 a 3
1073
B. What proportion has pulse rates between 65 and 90? — _ 1 o 5t 0 ~ ‘1 O
1P e 5 \ 5 L a 1. lg? :
a q>(no.%34£z, {’3'5)’; (9631:;
“’10 (10 O.l103r 0,4073%: C. Find the 80th percentile. £44,001: X0: O.%4(l‘5)+’\0 10 X5
Z
20: on D. If 30 people are randomly selected what is the probability that the average pulse
rate for this group is more than 73? a nB~lU
‘PCx7'Ioj—23t’ta7 \15/6317); (DEW
<Pt27 Hal 2 5~ “’43 @ (10 marks)
IV. A. The weights of parrot fish are normally distributed with a standard deviation of 0.9 kg. A random sample of 34 parrot ﬁsh had a mean weight of 3.0 kg.
Test at (x 2 0.1 to see if the mean weight of these ﬁsh exceeds 2.9 kg. uo 1C1 0.65:? l.7e<é9, WA [3Tth 6 W JUL/UL M Page 2 of 3
builﬁgﬁaﬁt _¢4e4nJLeﬂ/a g2: a} kigp {3 B. A four year study of various brands of bottled water found that 30% of the brands
of bottled water was just tap water. Let x : number of brands that are just tap
water. A random sample of 5 brands of bottled water is obtained. r
i. Fiud P(x = 2) c
L: ’ L 3
was m : aw
i Find the probability that at most one of the bottles is just tap wateri (i
a , o + p c l C
@CXAJB' PM ‘34
. ,— / 
r‘ ' b ‘3 < > _  S ;J\ <g 1
MD 67> @365 ‘l L L
O I l
_ /
o.lb%tﬂ k 0390b
iii. If the size of the random sample is 47 { 4 [
FindP(xsl6) 4513:4qu : ’ gray ;
t " _ . l
g, 157,4 .lV _,
4(Eéi ‘ “29(3540'791) “1794'
'$  l ‘\
t / M
//5/, _ g D 1, (A? (0 Ar
'4': I up;
[10 marks]
VV Computer repair times (in minutes) are exponentially distributed with 9 : 30 minutes.
A. Find the probability that the repair time is less than 25 minutes. @
a ,1 ﬂ 5L5“
QC X a a b) = \ ~59
: M . “b b .
l I 4 4 o . 5e 5’
Be What is the average repair time? v k
5 C v»
C. Draw a sketch of the distribution of repair times. @
z 3’
D. If random samples of 100 repair times are taken draw a sketch of the sampling
distribution of Y.
1 A
Lb
E. Calculate the probability that the mean repair time >? is no more than 28 minutes. \
<P<>< 4 1(3):? L7: L “so/mo :? L/ OE1>z [S — 01:1 4 Page 3 of 3 ...
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 Normal Distribution, Standard Deviation

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