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\hskip 1.5in \textbf{Midterm 1B--Stat 100--Spring 2001}   
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You may use calculators, but not books or notes. 
 Different parts of a problem have equal weight unless 
otherwise indicated.  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. (20 points) For the sample data 1,1,1,1,2,2,3 do the following. 
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(a)  Compute the median. 
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(b) Compute the average. 
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(c)  Draw a dotplot. 
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(d) Draw a histogram (be sure to label the axes so that the 
total area is 1). 
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 2.  (20 points)
Concerning the events $A$ and $B$, the following probabilities 
are given: 
$$
P(B) = \frac 14\ , \quad 
P(A|B) = \frac 12\ , \quad 
P(A|\overline B)= \frac 12 \ . 
$$
Determine 
(a) $P(AB)$, 
(b) $P(A\overline B)$, 
(c) $P(A)$, and (d)  $P(B|A)$. 
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(e)  Are $A$ and $B$ independent? Briefly justify your answer. 
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3.  (20 points)
Four students will be selected at random from a group of six 
juniors, eight sophomores, and four freshmen. \newline 
(a) What is the probability of selecting four freshmen? \newline 
(b) What is the probability of selecting two freshmen, one 
sophomore and one junior? 
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4.(15 points) 
For job applicants at Big Cheese Dairy, let $X$ denote the number 
of positions previously held by an applicant. Suppose $X$ has 
the following probability distribution (where $f(x)$ denotes the 
probability that $X=x$). 
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\begin{tabular}{|c||c|c|c|c|c|c|} \hline 
$x$ & 0 & 1 & 2 & 3 & 4   \\ \hline
$f(x)$ & 0.75 & 0.1 & 0.05 & 0.03 & 0.07  \\ \hline
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(a) What is the probability that an  
applicant has held at least two previous jobs? 
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(b) 
Compute $E(X)$.
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(c)  How many previous jobs altogether do you expect 1000 
job applicants to have held? 


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5. (15 points) For each part, answer TRUE or FALSE. 
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(a) If two events are mutually exclusive, then they must 
be independent. 
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(b) If the odds are 3 to 1 that there will be good weather tomorrow, 
then the probability of good weather tomorrow is 1/3. 
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(c) The model of Bernoulli trials is plausible in the following 
situation: a musical aptitude test is given to 10 students and the
times to complete the test are recorded. 
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6. (10 points) Suppose $E(X)=2$, the standard deviation of $X$ is 3, 
and $Y= 1-5X$. What is $E(Y)$? 

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