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\title{Stat 185 - Review problems for Exam 2}
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\noindent Our second exam is next Wednesday, October 25. Here are a few problems to get you thinking.
There's a good chance that \textit{most} or even all of these problems will be represented on the exam.
There might be one or two more, as well.

\begin{enumerate}
	\item I've got an unfair coin that comes up heads 75\% of the time. Suppose I flip that coin 12 times and count the number of heads.
	Use $n$ choose $k$ notation to express the probability that I get exactly 10 heads.

        \item According to the UNCA Factbook, of the 666 students enrolled as Freshmen in the Fall of 2016, 416 were women and 250 were men. If we randomly select 10 of
        those new students, what is the probability that exactly 4 of them will be men?

	\item 
	\begin{enumerate}
		\item Suppose I roll one fair, seven-sided die. \\ What  is the probability that I roll a 7 or an 8?
		\item Suppose I roll two fair, seven-sided die. \\ What  is the probability that I roll a 7 and an 8?
	\end{enumerate}

	
	\item Consider a random variable $X$ with the following distribution:
	
	\begin{center}
        \begin{tabular}{c||c|c|c|c}
            $X$ & -2 & 3 & 5 \\
    		\hline
            $P(X)$ & 0.2 & 0.3 & 0.5
        \end{tabular}
        \end{center}
        
        \begin{enumerate}
        		\item Write down the specific formula to compute $E(X)$.
		\item Write down the specific formula to evaluate $\sigma(X)$.
        \end{enumerate}
        
	\item Suppose that 10\% of all people are left handed. Use a normal distribution to estimate the probability that more than 15 people of a random sample of
	200 will be left handed.

	\item Suppose that, on average, the typical Stat 185 can make \$625 in a Summer job, with a standard 
	deviation of \$142. 
	\begin{enumerate}
		\item How much money would all 64 students enrolled in my Stat 185 classes \textit{expect} to make combined?
		\item What's the probability that, collectively, all 64 make more than \$55000 over the Summer
	\end{enumerate}
	
	\item In a random sample of 432 North Carolinians, I find that 85 of them smoke. 
	\begin{enumerate}
		\item What is the standard error associated with this measurement?
		\item Write down a 95\% confidence interval for the proportion of North Carolinians that smoke based on this data.
	\end{enumerate}

 	\item It is believed that nearsightedness affects about 8\% of 
            all children. In a random sample of 194 children, 21 are nearsighted.
                \begin{enumerate}
                \item Construct hypotheses appropriate for the following question: do these data 
                provide evidence that the 8\% value is inaccurate?
                \item What proportion of children in this sample are nearsighted?
                \item Show that the standard error of the sample proportion is 0.0195.
                \item What is the p-value for this hypothesis test? (Use R and/or a Z-score.)
                \item What is the conclusion of the hypothesis test?
            \end{enumerate}

\end{enumerate}


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