Download M_112Exam_1_Spring_2009KEY

Math 112 Exam 1 Name (PRINT) ________Key Spring 2009________
Good Luck! 100points
total
Show all work for full credit! Box your answers! Round to four decimal places! Write neatly with pencil!
I. Define or explain the meaning of the following: (2 points each)
a) Parameter: See book
b) Sample:
See book
c) Statistic:
See book
d) Population:
See book
e) Standard Deviation:
f) Random Sample:
See book
See book
II Give a specific example of the following types of data: (2 points each) (Answers may vary)
a) Qualitative Data:
Names like, Frank, Jim, Joe, Alex.
b) Quantitative Data: Distance like, height of Mount Everest.
c) Discrete Data: Number of keys on my key chain.
d) Continuous Data: Weights of books
III. Provide the appropriate notation for the following: (2 points each)
a) Symbol for the sample variance___ s 2 _____
b) Symbol for the population mean____  ___
c) Symbol for sample mean_____ x ____
d) Symbol for population variance____  2 ____
e) Symbol for standard deviation of the sample_____ s ___
f) Symbol for the standard deviation of the population____  ___
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IV. True or False (2 points each)
___T___Two events A and B are dependent if the occurrence of one effects the probability of
the occurrence of the other.
___F___Random Sample is a sample selected in such a way that allows every member of the population to
not have the same chance of being chosen.
___F___Mutually Exclusive events are independent.
___T___On some occasions the probability of an event can be 1.
___F___The probability of an impossible event is 1.
___T___ If a sample has a variance of 0.25, it’s standard deviation is 0.5.
__F___ The probability of event A or B is smaller than probability of event A and B.
___F____Mutually Exclusive events con occur at the same time.
____F___Mario calculated a probability and got 9/8. This is a possible answer in probability.
V. (10points total) Let E and F be two events of an experiment with sample space S. Suppose P(E)=0.4,
P(F )=0.7, and P(E∩F)=0.2. Compute:
________
(a) P ( E  F )  1  P( E  F )  1  {P( E )  P( F )  P( E  F )}  1  (0.4  0.7  0.2)  1  0.9  0.1
(b) Show why P(E and F) are not independent. Hint: Independence rule.
P( E  F )  P( E ) P( F )
They are not independent because: 0.2  0.4(0.7)
0.2  0.28
VI. The table below describes the smoking habits of a group of asthma sufferers. (10 points total)
Nonsmoker Occasional Regular
Heavy
Total
Smoker
Smoker
Smoker
Men
384
33
64
49
530
Women
349
44
72
38
503
Total
733
77
136
87
1033
a) If one of the 1033 people is randomly selected, find the probability that the person is a man or a heavy
smoker
P( Man  HeavySmo ker)  P( Man)  P( HeavySmo ker)  P( Man  HeavySmo ker)
530
87
49


 0.55 or 55%
1033 1033 1033
b) If one of the 1033 people is randomly selected, find the probability that the person is a man given is a
heavy smoker.

49
P( Man  HeaveSmo ker)
49
P( Man | HeavySmo ker) 
 1033 
 0.5632 or 56.32%
87
P( HeavySmo ker)
87
1033
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VII. (a, b, c, d, f =2pts each; e= 5pts) The Down Jones Industrial Average
Yearly Returns are on the right table. Find the following:
a) Find the mean.
{6.18  (7.1)  (16.72)  25.32  3.15  (0.61)  16.29  6.43  (33)}%
x
9
 1.3844%
b) Find the mode: No Mode
c) Find the median: -0.61
Year
Percent
Gain or
Loss
2000
-6.18%
2001
-7.10%
2002
-16.76%
2003
25.32%
2004
3.15%
2005
-0.61%
2006
16.29%
2007
6.43%
2008
-33%
d) Find the range: 58.32%
e) Find the variance: (show formula and plug in numbers from your calculator, than
work out the variance)
2 


n  x   x 
2
n(n  1)
2

9  (2416.6060)  (12.46)
21594.2024


98
72
2
 2  299.9195% 2
f) Find the standard deviation.    2  299.9195  17.3182%
VIII. (5 points) Use the empirical rule. IQ scores have a bell shape distribution with mean 100 and a standard
deviation of 15. Approximately what percentage of IQ scores is between 70 and 130?
One standard deviation from the mean : x  s  100  15  85, 115
Two standard deviation from the mean : x  2s  100  2(15)  70, 130
Approximately 95 % of the IQ scores are between 70 and 130
IX. (5 points) 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 73. Convert Frank’s score to a z-score.
x  x 73  73
Z

0
s
9
X. (5 points) Circle the right answer.
1) The following set of data represents letter grades on a test in a Statistics class:
A,A,A,B,B,B,B,B,C,C,C,C,C,C,C,C,C,CC,D,D,D,D,F.
Select the most appropriate measure of central tendency for the data described
a) Mean
b) Median
c) Mode
d) Midrange
2) The measure most affected by extreme values is:
a) Mean
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b) Median
c) Mode
d) Midquartile
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