12. A certain type of weapon has probability \( p \) of working successfully. We test \( n \) weapons, and the stock pile is replaced if the number of failures, \( X \), is at least one. How large must \( n \) be to have \( P[X \geqslant 1] \doteq 0.99 \) when \( p=0.95 \) ? (a) Use exact binomial. (b) Use normal approximation. (c) Use Poisson approximation. (d) Rework (a) through (c) with \( p=0.90 \).
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- We need to find \( n \) such that \( P[X \geq 1] \approx 0.99 \). - The probability of success for each weapon is \( p \). - The probability of failure for each weapon is \( q = 1 - p \). Show moreā¦
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