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2o09 - NAME STUDENT NUMBER STA22OH5F L0101 University of...

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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.l10|3r 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/ O-E1>z [S — 01:1 4 Page 3 of 3 ...
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