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\title
Midterm 1B--Stat 100--Fall 1996    
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You may use calculators, but not books or notes. Each problem is 
worth 20 points. Do not spend too much time on any one problem. 
 Put a box around the final answer to a question. 
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1.  
Given is the following sample data: 
25, 6, 1, 7, 13 , 5.  
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For this data, 
calculate the following (5 points each):  
(a)  the sample mean, 
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(b)  the sample standard deviation, \ \ 
(c)  the median, \ \    
(d) the interquartile range.
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2.    Determine which of the following are legitimate probability 
distributions. 
Give reasons for your decisions. 
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\hskip 1in (A) 
\hskip 1.2in (B)
\hskip 1.2in (C) 
\hskip 1.2in (D) 
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\hskip .8in x\  \ \ \ f(x) 
\hskip .8in x\  \ \ \ f(x) 
\hskip 1in  x\  \ \ \ f(x)
\hskip .95in  x\  \ \ \ f(x)
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\hskip .8in 2\ \  \ \  1/3 
\hskip .8in -2\ \  \ \ -.1 
\hskip 1in \ 0\ \ \  \ .7
\hskip 1in \ 2\ \ \  \  1/3
 \newline 
\hskip .8in 4\ \  \ \ 1/3 
\hskip .8in -3\ \  \ \ .5 
\hskip 1in \ \ 2\  \ \ \ .3 
\hskip 1in \  4\ \  \ \ 2/3 
  \newline 
\hskip .8in 6\ \ \  \ 1/3 
\hskip .8in \ 6\  \ \ \ .6 
\hskip 1in \ -4\  \ \ \ .01
 \hskip 1in 6\ \  \ \ 0
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3. Suppose $A$, $B$ and $C$ are three events such that 
$B$ and $C$ are 
mutually exclusive, 
$A$ and $B$  are independent,  
P($A$)=.7 \ , \ \ \ P($B$)=.1 \ \ and  \ \  P($C\overline B$)=.3 . 
 
Calculate the following: 
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a. P($BC$) \qquad \quad 
b. P($A|B$)\qquad \quad 
c. P($A\cup B$)\qquad \quad 
d. P($B|\overline A$)
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4. An IRS agent receives a batch of 15 tax returns that were flagged
by computer for possible tax evasions.  Of these returns, 
6 have illegal deductions and the other 9 are in good
standing.  Suppose the agent randomly audits 4 of these returns. 
Compute the probabilities that 
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a. none of the returns with illegal 
deductions are selected 
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b. at least two of the returns with illegal deductions are selected.
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5. In a certain batch of inferior firecrackers, the probability that 
a firecracker explodes when lit is only .3.  
Rosco will light 25 of these firecrackers.  
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a. What is the probability that exactly 10 of them explode? 
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b. What is the probability that at most 10 explode? 
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c. What is the probability that at least 10 explode? 
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d. What is the expectation of the number which will explode? 
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