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Midterm 1A--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: 
5, 5, 5, 2, 3.   For this data: 
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(a) (15 pts.) Calculate  
the sample mean,  
sample standard deviation, and  
median.  
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(b) (5 pts.) Draw a histogram, with bin (interval) length one. 
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Indicate your 
scale on the y-axis.  
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2(a)   Suppose $X$ is a random variable with mean 2 and 
with standard deviation 3.  Let $Y=X-5$. 
What are the mean and standard deviation of the 
random variable $Y$? 
 (No explanation required.) 
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(b)  Two fair dice are rolled. What is the probability 
that the sum of the numbers rolled is 5? 
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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($A$)=.6\ ,  \ \ P($B$)=.3 \  and  \  P($C\overline B$)=.25 . 
 
Calculate the following: 
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a. P($C$) \qquad
b. P($\overline B|C$) \qquad 
c. P($B|A$) \qquad
d. P($A\cup B$)
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4.  An instuctor will choose 4 problems from a set of 12 
containing 7  hard and 5 easy problems.  
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a. What is the probability she selects exactly two easy problems?
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b. What is the probability she selects at least one easy problem?
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5. A new drug cures a certain disease with probability .4 . 
Consider a random sample of 25 patients with this disease.  
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a. What is the probability that 15 or fewer of these people
will be cured? 
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b. What is the probability that exactly 15 will be cured? 
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c. What is the probability that at least 15 will be cured? 
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d. What is the expectation of the number of patients who will be cured? 


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