Stats 3Y03 Test #2 (Version 1)
November 7th, 2017
Name:___________________________________________
(Last Name)
(First Name)
Student Number:_____________________
This test consists of 18 multiple choice questions worth 1 mark each (no part marks), and 1
question worth 1 mark (no part marks) on proper computer card filling. Questions must be
answered on the COMPUTER CARD with an HB PENCIL. Marks will not be deducted for
wrong answers (i.e., there is no penalty for guessing). You are responsible for ensuring that your
copy of the test is complete. Bring any discrepancy to the attention of the invigilator. Only the
McMaster standard calculator Casio fx-991 MS or MS Plus is allowed.
1. The life of automobile voltage regulators has an exponential distribution with a mean life of
six years. You purchase a six-year old automobile with a working voltage regulator and plan
to own it for six years. What is the probability that the voltage regulator fails during your
ownership?
(a) .6321 (b) .5000
(c) .3679 (d) .1353 (e) .8647
2. A machine produces corks (for use in wine bottles) with diameters that are normally
distributed with mean 3 cm and standard deviation 0.1 cm. What percentage of such corks
are between 2.85 cm and 3.1 cm?
(a) 35.23%
(b) 9.18%
(c) 77.45%
(d) 84.16%
(e) 57.81%
3. The temperature reading from a thermocouple placed in a constant-temperature medium is
normally distrubited with mean ., the actual temperature of the medium, and standard
deviation 5. What would the value of 5 have to be to ensure that 95% of all readings are
within 0.1° of .?
(a) .034 (b) .051
(c) .503 (d) .317 (e) .019
4. Let 0 ÐBß CÑ œ 'Bß B !ß C !ß B C ". Find T Ð\ "3 Ñ.
(a) .3827 (b) .2593 (c) .2126 (d) .1875 (e) .1383
1
5. Consider the data set of systolic blood pressure readings for females (F) and males (M)
that is summarized in the Minitab output below. Approximately 29 males in the data set
have a blood pressure that is less than what value?
Descriptive Statistics: SYSTOLIC
Variable
SYSTOLIC
GENDER
F
M
Variable
SYSTOLIC
GENDER
F
M
(a) 130 (b) 141
N
39
39
N*
0
0
Mean
128.87
131.67
Q1
118.00
120.00
SE Mean
1.97
2.14
Median
128.00
130.00
Q3
138.00
141.00
StDev
12.31
13.33
Minimum
110.00
115.00
Maximum
156.00
163.00
(c) 138 (d) 118 (e) 120
6. The weight of a small candy is normally distributed with a mean of 5 g and a standard
deviation of 0.1 g. If 16 candies are placed in a package, what percentage of such packages
have a net weight that is less than 79 g?
(a) 10.61% (b) 3.29%
(c) 1.37% (d) 21.48%
(e) 0.62%
7. Consider the following data set.
12.5, 47.5, 25.1, 13.7, 31.2, 18.3
If we were to construct a normal probability plot for this data set, which of the following
would be one of the points on the plot?
(a) ÐÞ#"ß ")Þ$Ñ (b) ÐÞ#"ß #&Þ"Ñ
(c) ÐÞ'(ß "$Þ(Ñ (d) ÐÞ'(ß %(Þ&Ñ
(e) Ð!Þ#"ß "$Þ(Ñ
8. Let \" ß \# ß á ß \( denote a random sample from a populaton having mean . and variance
5# . Which of the following are unbiased estimators of .?
s" œ #\" \$ %\'
(i) @
(
s# œ #\" \# $\(
(ii) @
%
s$ œ #\$ $\' #\(
(iii) @
$
(a) all of them (b) (i) only (c) none of them (d) (ii) and (iii) only (e) (i) and (ii) only
9. In order to estimate the mean lifetime of a 75-watt light bulb, 50 bulbs were tested and the
following *)% confidence interval was produced: Ð"!!&Þ('ß "!##Þ#%Ñ. What was the
sample standard deviation?
(a) 15 (b) 25
(c) 50 (d) 45 (e) 55
2
10. Suppose that the random variable \ has the following distribution.
0 ÐBÑ œ #Bß ! B "
Suppose that a random sample of 8 œ % is selected from this distribution. Find the variance
of \ .
"
(a) "#
"
(b) #%
"
(c) $'
"
(d) (#
"
(e) ")
11. Which of the following is a correct stem and leaf plot?
(a)
(b)
Stem-and-leaf of C1 N = 10
Stem-and-leaf of C1 N = 10
Leaf Unit = 1.0
Leaf Unit = 1.0
4 2 1236
(3) 3 245
3 4 13
1 5
1 6
1 7 4
4 2 1236
(3) 3 245
3 4 13
0 5
0 6
1 7 4
(c)
Stem-and-leaf of C1 N = 10
Leaf Unit = 1.0
(d)
Stem-and-leaf of C1 N = 10
Leaf Unit = 1.0
4 2 1236
7 3 245
(2) 4 13
1 5
1 6
1 7 4
4 2 1236
3 3 245
(2) 4 13
0 5
0 6
1 7 4
(e)
Stem-and-leaf of C1 N = 10
Leaf Unit = 1.0
4 2 1236
(3) 3 245
2 4 13
0 5
0 6
1 7 4
3
12. Suspension helmets used by motorcycle riders and automobile race-car drivers are subjected
to an impact test in order to estimate the percentage of such helmets that are damaged. What
is the minimum sample size required if we wish to be 97% confident that the error in
estimating this percentage is less than .02?
(a) 3261 (b) 2652
(c) 2209 (d) 2944 (e) 2157
13. The elasticity of a polymer is affected by the concentration of a reactant. When low
concentration is used, the mean elasticity is 55, and when high concentration is used, the
mean elasticity is 60. The standard deviation of elasticity is 4, regardless of the
concentration. If two random samples of size 16 are taken, find the probabitliy that
\ high \ low #Þ
(a) .8556 (b) .8860
(c) .9082 (d) .9214
(e) .9830
14. The solar energy consumed (in trillion BTU) during 4 selected years in the United states was
&&Þ#*ß &*Þ(#ß '#Þ'*ß '$Þ)*
Find a 95% confidence interval for the mean yearly solar energy consumed.
(a) (55.89, 64.90) (b) (56.64, 64.15)
(e) (56.32, 64.48)
(c) (54.30, 66.49) (d) (55.08, 65.71)
15. Let 0 ÐBß CÑ œ #/BC ß ! B C. Find the marginal probability distribution of ] .
(a) /C Ð/C "Ñß C ! (b) #/C ß C ! (c) #/C Ð" /C Ñß C ! (d) /C ß C !
(e) #/#C ß C !
16. A batch of electrical components are tested and 85% of them lasted longer than 1000 hours.
Based on this data a confidence interval was then produced to estimate the proportion of such
electrical components that last longer than 1000 hours. One of the below intervals is the
confidence interval that was produced. Which one?
(a) ÐÞ)$(ß Þ)&'Ñ
(b) ÐÞ)%#ß Þ)&"Ñ
(c) ÐÞ)!)ß Þ)('Ñ (d) ÐÞ)$%ß Þ)'!Ñ
17. Let 0 ÐBß CÑ œ B Cß ! B "ß ! C ". Find IÐ\] Ñ.
(a) $#
(b) "
(c) "%
(d) "$
(e) "#
4
(e) ÐÞ)"*ß Þ))"Ñ
18. Suppose that 20% of people who are exposed to a certain bacteria become ill. If 500 people
are exposed to the bacteria, find the approximate probability that at least 90 of them become
ill.
(a) .7885 (b) .8265
(c) .8341 (d) .8790 (e) .7501
19. Correctly fill out the bubbles corresponding to all 9 digits of your student number, as well as
the version number of your test in the correct places on the computer card.
Note: You are writing Version 1.
Hint:
5
Answers (Version 1):
1. a 2. c 3. b 4. b 5. b 6. e 7. c 8. a 9. b 10. d
11. a 12. d 13. e 14. c 15. c 16. e 17. d 18. d
10
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