“An Aggie does not lie, cheat, or steal or tolerate those who do.”
EXAM 1 – FORM A
STAT 211
SPRING 2005
Consider a family with a mother, father, and two children. Let
A1={mother has influenza},
A2={father has influenza},
A3={first child has influenza},
A4={second child has influenza},
B={ at least one child has influenza},
C={ at least one parent has influenza},
D={ at least one person in the family has influenza}.
Suppose that P(A1)=0.10, P(A2)= 0.10, P(A1A2)=0.02, P(A3)=P(A4)=0.20, P(A3A4)=0.10.
Answer questions 1 to 8 using the information here.
1. Which of the following explains the wording in A1A2?
(a) Either the mother or the father has influenza
(b) Both the mother and the father has influenza
(c) Neither the mother nor the father has influenza
(d) At least one parent has influenza
2. Which of the following is the calculated P(C)? (P(C) is the probability of at least one parent having
influenza)
(a) 0.02
(b) 0.08
(c) 0.10
(d) 0.18
(e) 0.20
P(C)=P(either the mother or father or both has influenza)=P(A1)+P(A2)-P(A1A2)=0.10+0.10-0.02=0.18
3.
Which of the following is the probability that the mother having influenza but not the father?
(a) 0.02
(b) 0.08
(c) 0.10
(d) 0.18
(e) 0.20
P(A1A2’)=P(A1)-P(A1A2)=0.10-0.02=0.08
4.
If the first child has an influenza, which of the following is the probability of the second child having influenza?
(a) 0.10
(b) 0.20
(c) 0.50
(d) 0.80
(d) 0.90
P(A4 | A3)= P(A3A4)/ P(A3)=0.10/0.20=0.50
5.
If exactly one child has an influenza, which of the following is the probability of both child having influenza?
(a) 0
(b) 0.08
Not possible at all
(c) 0.10
(d) 0.20
(e) 1
Suppose there are many families with the same structure (mother, father, two children) observed. Use this
additional information to answer the next 3 questions.
6. If there are four mothers independently selected, which of the following is the probability that all of four
mothers having influenza?
(a) 0.0001
(b) 0.001
(c) 0.01
(d) 0.10
(e) 0.40
P(1st mother and 2nd mother and 3rd mother and 4th mother has influenza) = (0.1)4=0.0001 by
independence
7. If there are four mothers independently selected, which of the following is the probability that only the first
selected mother having influenza not the other three?
(a) 0.0009
(b) 0.0081
(c) 0.0486
(d) 0.0729
(e) 0.09
By independence, P(first mother has)P(but not the other three mothers)=0.10(0.9)3=0.0729
8. If there are four mothers independently selected, which of the following is the probability that exactly two
mothers having influenza not the other two?
(a) 0.0009
(b) 0.0081
(c) 0.0486
(d) 0.0729
(e) 0.09
 4
By independence and considering possibilities,   P(two mothers have)P(but not the other two
 2
2
2
mothers)=6(.10) (0.9) =0.0486
“An Aggie does not lie, cheat, or steal or tolerate those who do.”
EXAM 1 – FORM A
STAT 211
SPRING 2005
9. If you have a discrete data set and you like to create a histogram, which of the following should be used on
the vertical axis of the histogram? (the most correct answer should be chosen)
(a) Only frequency
(b) Only relative frequency
(c) Only density
(d) Either frequency or relative frequency
(e) Neither frequency nor relative frequency
10. If you have an interval data with the interval width 2 and density 0.2 on the 3rd interval, which of the
following is the frequency in the 3rd interval where there are 10 data points in the complete data?
(a) 2
(b) 4
(c) 10
(d) 20
(e) 40
Density=(relative frequency)/(interval width) where relative frequency is frequency/sample size.
Then 0.2=frequency/20
A survey is done to compare the base salaries (in hundreds of thousands of dollars) of chief executives in two
industries. The results are as follows.
Industry1 4.6
5.4
5.6
4.8
5.6
5.7
5.6
5.7
Industry2 14.3
4.1
21.5
3.3
8.1
5.6
9.7
The following is the related descriptive statistics and boxplots from SPSS.
Descriptive Statistics
Industry1
n
8
Minimum
4.6
Maximum
5.7
Mean
5.375
Standard deviation
.4301
Skewness
-1.323
Industry2
7
3.3
21.5
9.514
6.4788
1.175
Boxplot
20.0
15.0
10.0
5.0
Industry1
Industry2
Use all information given for industries to answer questions 11 to 19.
11. In which industry, the average salary is higher?
(a) Industry 1
(b) Industry 2
Either looking at the median on the boxplot or the means give the same information
12. In which industry, there is less variability in the salaries?
(a) Industry 1
(b) Industry 2
“An Aggie does not lie, cheat, or steal or tolerate those who do.”
STAT 211
EXAM 1 – FORM A
SPRING 2005
Either looking at the interquartile range (rectangle) on the boxplot or the standard deviation give the
same information
13. In which industry, there is an outlier in the salaries?
(a) both industries
(b) Industry 1
(c) Industry 2
(d) none of the industries
No need to compute just look at the boxplot. If there is it would be shown with circles.
14. Which of the following defines the skewness in the salaries for the Industry 1?
(a) Negatively skewed
(b) Positively skewed
(c) Symmetric
Either boxplot or the skewness measure give the same information.
15. Which of the following defines the skewness in the salaries for the Industry 2?
(a) Negatively skewed
(b) Positively skewed
(c) Symmetric
Either boxplot or the skewness measure give the same information.
16. Consider both industries, which of the following is the proportion of salaries higher than 5.6 (in hundreds of
thousands of dollars)?
(a) 0.25
(b) 0.38
(c) 0.40
(d) 0.57
(e) 0.67
15 data points in both industries where only 6 higher than 5.6 then proportion is 6/15
17. Consider only industry 1, which of the following is the proportion of salaries higher than 5.6 (in hundreds of
thousands of dollars)?
(a) 0.25
(b) 0.38
(c) 0.40
(d) 0.57
(e) 0.67
8 data points in industry 1 where only 2 higher than 5.6 then proportion is 2/8
18. Which of the following is the mode of salaries in Industry 1?
(a) 4.6
(b) 4.8
(c) 5.4
(d) 5.6
Most repeating data point
(e)5.7
19. Let’s divide the salaries in the second industry by 4 to deal with smaller numbers. Would this effect the
variance?
(a) Yes. 4 times higher variance
(b) Yes. 16 times higher variance
(c) Not at all
(d) Yes. 25% lower variance
(e) Yes. 6.25% lower variance
X: salaries then Y=X/4 then the mean of Y is mean of X / 4. Look at the formulas and see that variance of
2
_


_
1
 x x
2
Y is variance of X divided by 16 because       ( x  x) where 1/16=0.0625.
4
4
16




We will observe 3 customers paying the monthly phone bill in full (F) or not (N). (1st customer, 2nd customer,3rd
customer) will be used to show the outcomes in notation. In this experiment, the sample space will have 8
outcomes, S={(F,F,F),(F,N,N),(N,F,N),(N,N,F),(F,F,N),(F,N,F),(N,F,F),(N,N,N)}. Let’s define
A:at most 2 customers pay the monthly bill in full={(F,N,N),(N,F,N),(N,N,F),(F,F,N),(F,N,F),(N,F,F),(N,N,N)}
B: at least 2 customers pay the monthly bill in full={(F,F,F),(F,F,N),(F,N,F),(N,F,F)}
Answer the following 3 questions using this information.
20. Which of the following is the number of outcomes in AB?
(a) 3
(b) 4
(c) 6
(d) 7
(e) 8
AB={(F,F,F),(F,N,N),(N,F,N),(N,N,F),(F,F,N),(F,N,F),(N,F,F),(N,N,N)}
“An Aggie does not lie, cheat, or steal or tolerate those who do.”
STAT 211
EXAM 1 – FORM A
21. Which of the following is the number of outcomes in AB?
(a) 3
(b) 4
(c) 6
(d) 7
AB={(F,F,N),(F,N,F),(N,F,F)}
SPRING 2005
(e) 8
22. Which of the following is the number of outcomes in AB’? (Remember that B’ is B complement)
(a) 3
(b) 4
(c) 6
(d) 7
(e) 8
AB’={(F,N,N),(N,F,N),(N,N,F),(N,N,N)}
A chain of stereo stores is offering a special price on complete set components (receiver, compact disc player,
speakers, cassette deck). A purchaser is offered a choice of manufacturer for each component:
Receiver:
Kenwood, Onkyo, Pioneer, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers:
Boston, Infinity, Polk
Cassette Deck:
Onkyo, Sony, Teac, Technics
Use this information to answer questions 23 to 24.
23. Which of the following is the number of ways that only the receiver is Onkyo in the complete set selected?
(a) 9
(b) 12
(c) 18
(d) 27
(e) 30
(1)(3)(3)(3)=27
24. Which of the following is the number of ways that the complete set selected contains only two Onkyo
component?
(a) 9
(b) 12
(c) 18
(d) 27
(e) 30
Receiver and the compact disc player is Onkyo = (1)(1)(3)(3)=9
Receiver and the cassette deck is Onkyo = (1)(3)(3)(1)=9
compact disc player and the cassette deck is Onkyo = (4)(1)(3)(1)12
total of those possibilities=30
25. The two datasets are the salaries (in thousands of dollars) of 1000 employees and the number of bedrooms
in their houses. Which of the following should be used to compare the variability in these two datasets?
(a) Variance
(b) Standard deviation
(c) Interquartile range
(d) Coefficient of variation
(e) Any of the above
Since they do not have the same units, unit free measure should be used