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Unformatted text preview: MATH 1131 MIDTERM
Wednesday, November 3; 50 minutes NAME: V SOLUTION S
TAN STUDENT NUMBER: There are 6 questions on this test, worth a total of 50 points. The questions are in no particular
order. Make sure that you show your work (when this is possible). When asked for comments in a ques
tion, do so succinctly, and you may use point form if you wish. We will be looking for a correct answer, not a lengthy answer. ’ i The last page contains the probability distributions for discrete RVs and you may detach it from
the rest of the test. You may also use this page as scrap paper. You may Write on the back of the pages if you run out of space. Good Luck! 1. F T (2 marks each) Determine whether each of the following statements is true or false (write
T or F beside each statement). For these questions you do not need to show your work. (a) A bivariate quantitative data set has a sample correlation of 0.1. It follows that there
is little or no relationship between the two variables in the data set. (b) Consider two events, A and B. The probability of event A is 0.6 and the probability of
event B is 0.7. It follows that the two events cannot be independent. (c) In medicine, a false positive occurs when a subject tests positive for a disease but is
actually negative for the disease. Health Canada is developing a new test for H1 N1.
By controlling the probability that a person with H1 N1 tests positive as well as the
probability that a person without H1 N1 tests negative, Health Canada can keep the
number of false positives small. _(d) The current median income in Toronto is 23,000 annually. It is possible to alter the
income of 95% of Toronto’s population and not change the median.  (e) The current mean foFincomes in Toronto is 30,000. Suppose that everyone in
Toronto receivesa raise of 5%. After the raise, the mean for incomes in Toronto _ is;'31,500. 2. A large cell phone company believes that 5% of its products are defective. Two quality
control inspectors visit this company and test their product. (a) The first inspector tests the products one by one (each product is randomly selected
from the company's large warehouse), and stops once a defective cell phone is
found. (i) (3 marks) Find the probability that the inspector tests exactly 1: products for
k = 1, 2, 3. ch=k):ap)""P k>xl f,=o.o:5 POM) = 0.05 = P(x=a) = o.ouﬁz5 (ii) (2 marks) Suppose that the inspector charges $100 per item inspected. How
much does the company expect to pay for the inspection? .I00.L —=_LQO_= 000
m P) 0.05 2's; (b) (5 marks) The second inspector also tests the products one by one, where each
product is randomly selected from the company’s large warehouse, and stops once
a defective cell phone is found. However, if she tests three products, and all three
products pass the inspection, she will also stop. Let X , denote the number of items
tested by the second inspector. Find the probability distribution of X. PM +hreo. pass): 0.353: 0.25%45
= l— (o.os+o.ou¥5+o.045125) POM) = 0.05
P(x=z) = coins
P(x=s)= omsrzs + 0.253325 = 0.3015 3. Several nights after Hallowe’en, Perrin's trick or treat bounty has 30 items left over. There
are 5 bags of chips, 10 chocolate bars, and 15 other candies. Perrin picks 6 treats at
random. (a) (2 marks) Find the probability that he picked exactly 3 bags of chips and 3 chocolate
bars.  __. 0302020863 (1") (b) (3 marks) Find the probability that he'picked all of the bags of chips. H 0.0000‘12l03‘lj 7 cozizw’ioN } 6 9. b 8’?! 4. For a data set of heights of sons and f ers ith a sample size of 1078, the sample
mean and variances were found to b d 7.5343 for the fathers and 68.6841 and 7.9225 for the sons. The correlation was . 13. son's height father's height (a) (3 marks) Find the regression line for sOns’ heights on fathers" heights and comment . ‘ '
on the scatterplot. /\  ‘ 5
. b = rs : 0.5013 1522 = 0.5m!
*3” . . H.534?) A * ﬁg _.. mm! —0. sun (61.6%!) = 35.98% regression line found above. SlopL 7 {or each. inch increase at fallwls [on aux/2% , Jrlm son‘s l‘nomaacs ha osml mam.
lnleralo‘l‘ ~) prank/HO“ wt X=D é as Such
. u) {5 Mass (iaexlraflola’hb 5. For men_, binge drinking is defined as having five or more drinks in a row. According to
a study by the Harvard School of Public Health, 44% of male college students engage
in binge drinking, 37% drink moderately, and the rest abstain entirely. Moreover, 17% of '
those who engaged in binge drinking have been involved in alcohol—related automobile:
accidents, and 9% of those who drink moderately have been involved in alcohol—related .
automobile accidents. ' (a) (3 marks) A male college student is randomly selected, what is the probability that
this student has not been involved in any alcoholrelated automobile accident? Polar I‘m/chad) = 0.1m oxarosfom + 0.13 . l
I = 0.88% (b) (3 marks) A randomly selected male college student has never been involved in an ' ~ .
' alcoholrelated car accident. What is the chance that he is a binge drinker? ' ' ' ~ ‘ ‘ 'l J :5 OHH.O£3
P (blnﬁp ( not "No va ) 038‘?) 2: OHDSB (c) (4 marks) Out of five randomly selected male college students, what is the probability
that exactly two have been involved in alcohol—related automobile accident? x~ 5mm (rt.5 , p = l—oxala) P 0:2) = "#07055 = 0.0223 1 6..T he stemandieaf plot beiow shows the number of home runs hit by Mark McGuire during
the 19862001 seasons. 0 5 28 29
22399
29 O‘NwhmmV 399 (a) (2 marks) Comment on the histogram for this data set. Um'modaL
swbdc ,
no 00H t «21 s (b) (3 marks) Find the fivenumber summary for this data set. moux=¥0
mm=5 ice 0% Qt —7 0.25 (“Nor—9.25
Qt '= 2.2+ 0.15 (26—22.) = 93.45 logeg mum a 0.35 (m) —— m as MEDIAN = 65%?! = as
2 ioczr? Q3 9 ‘0‘}510HIB‘: 12.}5
62% I: 49 + 0.45 ((2433 = $.25 3 9335 as $1.25 370 (c) (2 marks) Are there any outliers in this data set?' = n?5 = l.5x IQE: 4.25 stZS =325 no outliers (d) (3 marks) Mark’s mean number of home runs was 36.44 with a standard deviation of
19.65. Calculate the proportion of data that lies within two standard deviations of the
mean. Compare this with the proportion of data that should lie in this interval based
on the empirical rule.   scum +£03.95) = 35.4% 353%  103.653 par—“2.34:
a “90520 oQlhadata (Lu Elia £478 01? m man
’7 empm'cd mUL sags 411/13 shouldha “@899 :. Hill‘s claimsd has M1040 ‘ial’ls
“tan Paciﬁc/Rd 108 CL
balk shaped Al‘st‘n MATH 1131 MIDTERM
Wednesday, November 3; 50 minutes NlllTE STUDENT NUMBER: There are 6 questions on this test, worth a total of 50 points. The questions are in no particular
order. Make sure that you show your work (when this is possible). When asked for comments in a ques
tion, do so succinctly, and you may use point form if you wish. We will be looking for a correct
answer, not a lengthy answer. : The last page contains the probability distributions for discrete RVs and you may detach it from
the rest of the test. You may also use this page as scrap paper. You may write on the back of the
pages if you run out of space.  Good Luck! 1. A large cell phone company believes that 3% of its products are defective. Two quality
control inspectors visit this company and test their product. (a) The first inspector tests the products one by one (each product is randomly selected from the company’s large warehouse), and stops once a defective cell phone is
found. (i) (3 marks) Find the probability that the inspector tests exactly k products for
k = 1, 2, 3. xiv Wk (p = 0.0%) 17 (M) = 0.03
P(x=z) = 0.01m Peas) = 0.02.922? (ii) (2 marks) Suppose that the inspector charges $85 per item inspected. How
much does the company expect to pay for the inspection? 35 = £2883. as $ (b) (5 marks) The second inspector also tests the products one by one, where each
product is randomly selected from the company’s large warehouse, and stops once
a defective cell phone is found. However, if she tests three products, and all three
products pass the inspection, she will also stop. Let X denote the number of items
tested by the second inspector. Find the probability distribution of X. QU
.9.
()0
‘9
0“
m
._/
n
0
L9
.u
0.)
ll
P
‘i’
N
6‘
4.)
w POM) = 0.03 P r 0.02.3 I P(X= 3) = 0 0282.2? + 0.812643
tome?) 2. (2 marks each) Determine whether each of the following statements is true or false (write
T or F beside each statement). For these questions you do not need to show your work. F (a) A bivariate quantitative data set has a sample correlation of +0.01. It follows that
there is little or no relationship between the two variables in the data set. F (b) Consider two events, A and B. The probability of event A is 0.6 and the probability of
event B is 0.3. It follows that the two events must be independent. (c) In medicine, a false positive occurs when a subject tests positive for a disease but is
actually negative for the disease. Health Canada is developing a new test for H1 N1.
F By controlling the probability that a person with H1 N1 tests positive as well as the
probability that a person without H1 N1 tests negative, Health Canada can keep the number of false positives small. T (d) The current mean income in Toronto is 30,000 annually. It is possible to alter the
income of 0.01% of Toronto’s population so that the resulting mean is 300,000 annu ally. T (e) The current interquartile range for incomes in Toronto is 150,000. Suppose that
everyone in Toronto receives a raise of 5%. After the raise, the interquartile range
for incomes in Toronto is 157,500. 3. An urn contains 20 balls of which 5 are green, 5 are blue, and the rest are purple. You
select 6 balls at random. (a) (2 marks) Find the probability that you select exactly 3 green balls and 3 blue balls. (260 = 0.0025454?) (b) (3 marks) Find the probability that you seleCt all of the green balls. S 15) :.
f___L__ *. 00005866663
20
b 4. The stemand—Ieaf plot below shows the number of home runs hit by Mark McGuire during
the 19862001 seasons. 0 5 28 29
22399
29 O—LNOObmouw 399 (a) (2 marks) Comment on the histogram for this data set. (b) (3 marks) Find the fivenumber summary for this data set. SAME its TAN (c) (2 marks) Are there any outliers in this data set? (d) (3 marks) Mark’s mean number of home runs was 36.44 with a standard deviation of
19.65. Calculate the proportion of data that lies within two standard deviations of the
mean. Compare this with the proportion of data that should lie in this interval based
on the empirical rule. with a sample size of 1078, the sample
d 7.5343 for the fathers and 68.6841 and 5. For a data set of heights of sons and .  mean and variances were found to b father's height son's height (a) (3 marks) Find the regression line for fathers’ heights on sons’ heights and comment
on the scatterpiot. /\
5: L54 = 0.5023 955% = 03833
A
0L Sx 9.8225
:42; = 6?.mle M888 (sum) =awss (b) (2 marks) Provide an interpretation of the coefficients (slope and intercept) in the
regression line found above. 886 TAN 6. For men, binge drinking is defined as having five or more drinks in a row. According to
a study by the Harvard School of Public Health, 44% of male college students engage
in binge drinking, 37% drink moderately, and the rest abstain entirely. Moreover, 17% of
those who engaged in binge drinking have been involved in alcoholrelated automobile
accidents, and 9% of those who drink moderately have been involved in alcoholrelated
automobile accidents. (a) (3 marks) A male college student is randomly selected, what is the probability that
this student has not been involved in any alcoholrelated automobile accident? gee TAN (b) (3 marks) A randomly selected male college student has never been involved in an
‘ralcohol—related car accident. What is the chance that he is a binge drinker? (c) (4 marks) Out of five randomly selected male college students, what is the probability
that exactly two have been involved in alcoholrelated automobile accident? ...
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This note was uploaded on 01/23/2012 for the course MATH 1131 taught by Professor Wong during the Fall '10 term at York University.
 Fall '10
 Wong
 Statistics

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