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Problem 38

Let \(X \sim \mathrm{B}(n, p)\). Use the CLT to find \(n\) such that: $P[X>n / 2] \leq 1-\alpha\(. Calculate the value of \)n\( when \)\alpha=0.90\( and \)p=0.45$.

Expert verified

The value of \(n\) should be approximately 33.

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Chapter 2

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$$
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline X=x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline P(X=x) & k & 3 k & 5 k & 7 k & 9 k & 11 k & 13 k & 15 k & 17 k \\
\hline
\end{array}
$$
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