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Unformatted text preview: TAT 515 Fall 2011——— Exam 1 Name: if ._ 1 .I . (20 points) In professional sports, stacking is a term used to describe the practice of
WVQ 352'" fricanAmerican players being excluded from certain positions because of race. Table l
i 5 elow summarizes the race and positions of 368 NBA players in 1993. _._."— Table 1 Position Totals White
African
American Totals Suppose an NBA player is selected at random from that year‘s player pool. (a) (5 points) What is the probability that the player is white or a center? (b) (5 points) Given that the player is white, what is the probability that he is a center? ﬂ .__L
'5 9+ (c) (10 points) Are the events {White player} and {Play center} independent? Explain. PE‘NN’ ?(CE~TM): (2:, 0163
it Waderlwfe/E) :4; (jaw. (a),
mafia, mm .th a] m we Cam] (the, bet Ar“ f . Fran 'taillw’t‘k 2. (20 points) Thirty students in an experimental psychology class use various techniques
to' train a rat to move through a maze. At the end of the course, each student’s rat is timed
as it negotiates the maze. The results (in minutes) are depicted in the following stemand
leaf display obtained from Minitab. For example, according to the display, the longest
running time is 9.7 minutes. StemandLeaf Display: RUNTIME Stem—and—leaf of RUNTIME N = 30
Leaf Unit = 0.10 1 0 6 8 1 0167799
12 2 0047
{6) 3 123678
12 4 0245 8 5 1236 4 6 0 3 7 6 2 8 2 1 9 7 (a) (5 points) According to the stemandleaf display, what is the median time among these
30 rats running through the maze? . ‘ . \ _ _ ‘ 1}] _ l 3 \ {)‘flt 0/ ,_. c Widthth die/x W if ml W2 :4. 3 E Wm?
4/? tie 55902.4( 5151:, x . my ‘5 I meltM :3 ﬂu}
(b) (5 mints) According to the Stemandleaf display, what is the ﬁrst quartile of running (0) (5 points) The mean and standard deviation of the running time of this group of rats are
3.74 minutes and 2.20 minutes, respectively. What is the zscore associated with the
longest running time of this group of rats? __ 97"3'71‘ a, 0‘"
Z... 226 W 2.7] (d) (5 points) Suppose that the zscore of the running time of a rat in this group is — 0.2
(negative 0.2). What is the running time (in minutes) of this rat? 1: 574 + 2.20 x(——o.2_) :53 (’muH) E1 03. (18 points) A sample space contains six sample points. Events A, B, and C as shown in the Venn diagram below. The probabilities of the sample points are P(1)=0.2,
P(2)=0.05, P(3)=0.3, P(4)=0.l, P(6)=0.25. (a) (6 points) Which pairs of events, ifany, are mutually exclusive? Explain.
BMW Ana :2 ¢, s0c=¢ W
A and C. m @CMME 1'1: , Jo we l5 aeml. C. (b) (12 points) Find the following three probabilities, PM”) , P(A u 8') , and
P(A" m B) l)(AC):l* l“) = l iP(l)+f(1)+P(3)} : 0+9!
“MB'74 PWr to” Few PM) 2 as,
FWﬂwzma=aL 
Mime 4f! 4. '25 points) Suppose that data on the number of fatalities in a month among U.S. airlines
_ a w e recorded during the pastt years, where t is a very large number so we have data from
kit(Mesa 4135 In, my years. According to the record, at most 4 fatalities were observed in a month in the
past t years. Table 2 below gives the percentage of all these recorded months that have
certain number of fatalities. For instance, the following table suggests that 30% of the time
there was no fatality in a month, and 36% of the time there were one fatality in a month.
Denote by X the number of fatalities in a month. Table 2 gives the probability distribution of x.
Table 2
x 0 1 2 3 4
P(x) 0.3 0.36 0.22 0.09 ‘9 j (a) (5 points) Suppose one month is randomly selected from all these recorded months.
What is the probability that there were 4 fatalities in this selected month? (This
corresponds to the questiOn mark in Table 2.) : ]_. (0.5+ Uéb+oyil+0voﬁ) : 0.05 (b) (10 points) Find the expected number of fatalities per month based on the probability
distribution depicted in Table 2 (and your answer in part a.). Interpret this expected value. /{:E(X)= 517001) I
.—. OX 0 5+ I XD56+ bail#:9053621. 410.05 '5 Hf] A a
.32 via 1mg my (712 itmét “Cc lace. M7 my W £22145 two ) has a a (‘3) (10 POimS) F ind the standard deviation of the number of fatalities in a month.
EL: var» = 1' [a —,t{)" Pg)
4 .L . ___ . (1 z X 0.22
:2 {ow/y?) x 0.5 + (PM?) X056+ (2 II/) + ('Bw—IJCD'Z mo? + (ZrHQ"! v 05
2 l. My 1
E 3.] 1»; e 2:. 1.03% E , I! 5‘ HS . (8 points) Suppose that I hand out a list of 10 questions, 5 of which will appear on the “a 1 na] exam of this course. You randoml choose 7 out of the 10 questions to study. 15 NW A _t e probability that 101.1 stu y a 3 questions that will appear on the ﬁnal exam“ (Hint: irst ﬁnd the number 0 ' ways to c oose questlons a omtionsmn ﬁnd the umber of ways to choose 7 questions with 5 of them appearing in the ﬁnal exam.) . £3 anberr 1/037} 01" 7' CW f0 :(’D)_, it}! :!__20 J 755*. Peat/é; A41 .5 are. Layt}: " a ' ' "' P M
gamma cue, 46 de 7th,“, I I a M' ?!th I
Lﬁrlzjtmlam:(5)~51[o——~ﬁamtfuez aa7‘ «  n w ._n>..__ “’ Rféi '" ‘ my] to ma A W/Xﬂ_ (9 points) [Does m 's diet inﬂuence baby '5 Sex?] Researchers from the universities of
Exeter and Oxford in England asked 740 ﬁrsttime moms in the United Kingdom to keep
food diaries before and during early pregnancy. The women didn’t know the sex of their
babies, but when researchers reviewed their food plans, they found that moms who consumed more calories of higher quality before conceiving were about 24 percent more
likely to give birth to boys than moms who ate less. (a) (3 points) Describe the population of interest in this study. 7&2 ﬁftuérsim a 119 (dele ‘71 Mt“ jig—fame MW at 75/112 Mk”. (b) (3 points) Describe the sample in this study. 741 (mfg mipm C71 740 mm 14th 4W; (0) (3 points) Identify the data collection method used for this study. QW( mad; _ ...
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