Q2
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Probability
└── Homework
└── W8
└── Q2.tex
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\begin{document}
\section*{Question 2}
\noindent During the rifle qualification in the Marine Corps the final ten shots are taken from $500$ yards. You receive one point for a hit and zero for a miss. If each shot is independent and the probability you hit is $p = 0.70$, what is the probability that you hit $7$ or more of your shots?
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\subsection*{Solution}
Let $X\sim\mathrm{Binomial}(n=10,p=0.70)$. We want
\[
\bP(X\ge7)=\sum_{k=7}^{10}\binom{10}{k}(0.70)^k(0.30)^{10-k}\approx0.650
\]
\subsection*{Answer}
\[\boxed{\bP(X\ge7)=\sum_{k=7}^{10}\binom{10}{k}(0.70)^k(0.30)^{10-k}\approx0.650}\]
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