STT315: Summer A 2017, Section 102
Mid Term: June 2, 2017
Multiple Choice Questions
Answer ALL questions.
Time: 60 mins
Name: __________________________
PID: _________ Username: _________
1. For a class the average score was 65, the median 67 and standard deviation 11. The
instructor decided to add 5 points to all the scores. After this addition of this 5 points
a) mean will change to 70, median will remain as 67 and the standard deviation
will change to be 16
b) mean will remain as 65, median as 67 and s.d. as 11
c) mean will change to 70, median will remain as 67 and the standard deviation
will continue to be 11
d) mean will change to 70, median to 72 and the standard deviation will change
to 16
e) mean will change to 70, median to 72 and the standard deviation will continue
to be 11
The box plots of the scores of 3 students (I, II, and III) are as follows:
2. The value of Q3 for student 1 is:
a) 30
b) 40
c) 50
d) 60
e) 70
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3. Which of the following is correct
a) The scores of student III are skewed to the right
b) The scores of student III are skewed to the left
c) The scores of student III are symmetric
d) Cannot say because the mean score is not known
e) Cannot say because there are outliers
4. Find the sample standard deviation of 8,3,1,1,0.
a) 6.76
b) 3.21
c) 15.00
d) 10.30
e) Cannot compute because the population mean is not known.
5. What is the median of 18,19.5,23.5,24.5,28,35,35.5,36,37.2,37,38,38,39,41,46.5?
a) 36
b) 36.6
c) 35.75
d) 38
e) none in the this list
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6. The figure above represents a frequency histogram of mileages for 32 cars in an
experiment to determine fuel consumption. Which of the following values could be
considered an outlier?
a) 42.3
b) 50.5
c) 36.0
d) 25
e) 20.7
7. Which of the following is true for the above histogram?
I Mean < Median
II Mean > Median
III Mean < Mode
IV Mean > Mode
a) II and III
b) II and IV
c) I and IV
d) I and III
8. The median of the histogram would be close to
a) 25
b) 29
c) 10
d) 27
e) Cannot say – we need the underlying data to compute the median
9. X is a normal random variable with mean 5 and standard deviation 10. Y is a normal
random variable with mean 10 and standard deviation 5. Which of the following
statements is correct?
a) The proportion of X within one standard deviation of its mean is smaller than
the proportion of Y that is within one standard deviation of its mean
b) The proportion of X within one standard deviation of its mean is same as the
proportion of Y that is within one standard deviation of its mean
c) The proportion of X within one standard deviation of its mean is larger than
the proportion of Y that is within one standard deviation of its mean
d) Cannot say without the use of normal distribution tables
e) Either a) or c)
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10. After the data was collected it was realized that there was an error and the
observatons in 42-44 were all actually in the 32-34 bin. If this change is incorportated
then for the resulting histogram
a) Mean would change but median would remain unchanged
b) Mean would remain unchanged but the median would change
c) Neither the median nor the mean would change
d) Both the mean and median would change
e) Cannot say, but the histogram is now bimodal
The following histograms represent four different datasets. Study these and answer
questions 11 and 12.
Histogram 1
Histogram 2
10
0
5
Frequency
15
20
Mileage of different car models, 1978
10
20
30
40
Mileage (mpg)
Histogram 3
Histogram 4
Values in 120 throws of a die
S&P 500, January 2001 - December 2001
-1 s.d.
mean
+1 s.d.
+2 s.d.
10,000
15,000
Volume (thousands)
+3 s.d.
+4 s.d.
15
10
Frequency
40
30
5
20
10
0
0
Frequency
50
60
20
-2 s.d.
5,000
20,000
25,000
0
2
4
values
Source: Yahoo! Finance and Commodity Systems, Inc.
11. Which one of the charts suggests that the data form a uniform distribution?
a) Histogram1 and Histogram2
b) Histogram 2
c) Histogram 3
d) Histogram 4
e) None of the histograms
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12. Which one of the charts suggests that the data come from a normal distribution?
a) Histogram 1
b) Histogram 2
c) Histogram 3
d) Histogram 4
e) All the histograms
13. What proportion and values do the interquartile range include?
a) 50% of the un-ranked values
b) 25% of the ranked values
c) 70% of the ranked values
d) 50% of the ranked values
e) 70% of the un-ranked values
14. Toss a coin two times. Let Hi be the event of the toss resulting in a head and Ti be
the event of getting a tail at the i-th toss for i=1,2. Which of the following is the event
of getting at least one head in the two tosses?
a) 𝑇1 ∪ 𝑇2
b) 𝑇1 ∩ 𝑇2
c) 𝐻1 ∪ 𝐻2
d) 𝐻1 ∩ 𝐻2
e) 𝐻1 ∪ 𝐻2 ∪ 𝑇1 ∪ 𝑇2
15. We roll a fair die with six faces and observe the face showing up at the top. So, the
possible outcomes are 1, 2, 3, 4, 5 and 6. The sample space of this experiment
a) Does not exist because we are rolling a die, not sampling
b) {1, 2, 3, 4, 5, 6}
c) An empty set
d) Is a table showing each value and its corresponding probability
e) None of the above
16. Consider the event A = {2, 3, 5}. Then P(A) =
a) 1/(2+3+5) = 1/10
b) 1/3
c) 1/2
d) 1/2 +1/3 + 1/5
e) 1
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17. Let B = {2, 4, 6} and C = {3, 6}. Then B and C are
a) Disjoint as well as independent
b) Independent, but not disjoint
c) Neither disjoint nor independent
d) Disjoint but not independent
e) Insufficient information, cannot say
A census of dorm rooms on a large college campus revealed that 40% had refrigerators,
55% had TVs, and 32% had both a TV and a refrigerator.
18. What is the probability that a randomly selected dorm room has “a TV or a
refrigerator”?
a) 0.95
b) 0.31
c) 0.22
d) 0.87
e) 0.63
19. What is the probability that a randomly selected dorm room has “a TV or a
refrigerator, but not both”?
a) 0.95
b) 0.31
c) 0.22
d) 0.87
e) 0.63
20. What is the probability that a randomly selected dorm room has “neither a TV nor a
refrigerator”?
a) 0.37
b) 0.63
c) 0.31
d) 0.95
e) 0.87
21. The event that “a dorm room has a TV” and “a dorm room has a refrigerator” are
a) Neither disjoint nor independent
b) Independent, but not disjoint
c) Both independent and disjoint
d) Disjoint but not independent
e) Insufficient information, cannot say
______
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