Math 112
Exam 1
Show work for full credit! Round to three decimal places! 100points total
Full Name _______________________
ID# ___________
Good Luck!
I. (2pts) Define the following:
a) Parameter:
See book definition.
b) Sample: See book definition.
c) Population: See book definition.
d) Frequency Distribution: See book definition.
e) Symmetric Distribution: Left half of histogram or curve is a roughly a mirror image of right,
~50% on each side.
f) Standard Deviation: See book definition.
g) Random Sample See book definition.
II. What is the difference between qualitative data and quantitative data, be specific. (3pts each)
Qualitative data can be separated into different categories that are distinguishable by some
nonnumeric characteristic.
Quantitative data consists of numbers representing counts or measurements.
Is the weight or height of your professor a qualitative data? Yes or NO
III. Provide the appropriate notation for the following: (1 point each)
a) Symbol for the population mean____  ___
b) Symbol for the sample mean___
x
__
c) Symbol for population variance___  ____
2
2
d) Symbol for sample variance__ s ___
e) Symbol for standard deviation of the population___
 ____
f) Symbol for the standard deviation of the sample___S_____
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IV. True or False (1pts each)
__T___Two events A and B are independent if the occurrence of one does not affect the probability of
the occurrence of the other.
___T__Random Sample is a sample selected in such a way that allows every member of the
population to have the same chance of being chosen.
___F__Mutually Exclusive events are events that CAN occur simultaneously.
___F__On some occasions the probability of an event can be negative.
___T__The probability of an event that is certain to happen is 1.
___T__If a sample has a variance of 2.324, it’s standard deviation is 1.524.
___F__If A is an event of a sample space with P( A)  P( A) , then P(A)=0.50.
___T__If a sample has a standard deviation of 4 then its variance is 16.
___T_ For any event A, the probability of A is between 0 and 1 inclusive.
___T__ Pr( at least one ) =1- Pr( None)
V. (2pts each, 12 total) Find the probability that when a couple has three children,
a. Among the three children , there is exactly one girl.
b. Among the three children, there is exactly two girls.
c. Among the three children, there is exactly three girls.
d. Among the three children, at least one girl.
e. Among the three children one or two girls
f. Among the three children, the complement of three girls.
Hint: Start with the sample space, there is 8 simple events in the sample space.
S={ GGG,GGB,GBG,GBB,BGG,BGB,BBG,BBB}
a)
3
8
d)
7
8
b)
3
8
c)
1
8
1 7
Note: 1- 
8 8
e)
6
3 3
6
Note: P(1G  2G)= P(1G)+P(2G)- P(1G  2G)=
+ -0=
8
8 8
8
f)
7
8
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VI. ( 4 points each, 8 points total)
Cause of Death
Heart Disease
Other
310
205
155
140
465
345
Cancer
135
55
190
Smoker
Nonsmoker
Total
Total
650
350
1000
Find the following two probabilities using the table above.
1) If one person is randomly selected, find the probability that he or she died of heart disease.
P(person died of heart attack)=
465
 0.465
1000
2) If one person is randomly selected, find the probability that he or she died of heat diseases given that
he or she was a nonsmoker. Hint: Conditional Pr.
P(died of heart attack  non somoker)
P(nonsomker)
155
1000  0.443
=
350
1000
P(died of heart attack | non somoker)=
VII. Use the sample data “Quiz 1 M112” from below to do the following. (2points each, 12 total)
25
20.5
19.5
a) Find the mean.
22.225
b) Find the mode:
NO MODE
c) Find the median:
22
d) Find the range:
16
27
19.75
29.5
23.5
13.5
29
e) Find the variance (show formula and plug in numbers from your calculator):
 
2
n(  x 2 )  (  x ) 2
n(n  1)

10(5215.312)2  (222.25)2
 30.645
90
f) Find the standard deviation of the Quiz data set.
  30.645  5.54
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15
VIII. (2points each, 10 total)
Interpret the 5-number summary from the Box Plot above. Note you will not get credit for just
putting down the 5 numbers; you must give meaning to them.
1._Minimun quiz score is 6__
2._Maximum quiz score is_ 29__
3._1st Quartile is 15. _This means that 25% of quiz scores are below 15 or 75% of scores above 15
4._2nd Quartile or Median is 20.125. This means that 50% of quiz scores are below 20.125 or 50%
of quiz scores are above 20.125_
5. _3rd Quartile is 24.875. This means that 75% of quiz scores are below 24.875 or 25% or quiz
scores are above 24.875_
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IV. (2 points each, 10 total)
Histogram (with Normal Curve) of " Quiz 1 M112"
Mean
StDev
N
7
19.53
6.647
36
6
Frequency
5
4
3
2
1
0
5
10
15
20
Scores
25
30
35
Above is a frequency table of our Quiz 1 scores. Note that there are 11 classes and the lower limit
starts at 3.75 and the class with is 2.50.
1. How many people in class received scores btw 6.25-8.75? __1__
2. Which class has the lowest scores and how many? __3.75 to 6.25, two students fall with in this
class._
3. How many people fall in the class score of 28.75-31.25?__3__
4. Say, the above graph is normally distributed, what scores values would encompass
approximately 95% of our Quiz 1. __ (6.236 ,32.82)___
5.
What do we call values that fall two standard deviation away from the mean?
____Unusual_________
V. (5pts) Scores on an Elementary Statistics test at Cerritos College have a mean of 73 and a standard
deviation of 9. Frank has a score of 91, John has a score of 73 . Convert Frank’s and John’s score to a
z-score.
Frank ' s score:
91-73
Z=
2
9
Professor Seres
John's score:
73-73
Z=
0
9
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