document.write( "Question 1092450: Suppose that for single launches of a space shuttle, there is a constant probability of O-ring failure (say, .15). Consider ten future launches, and let X be the number of those involving an O-ring failure. Use an appropriate probability model and evaluate all of the following:
\n" ); document.write( "a) P[x=2]
\n" ); document.write( "b) P[x>=1]
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\n" ); document.write( "d) Var X
\n" ); document.write( "e) standard deviation of X= \n" ); document.write( "

Algebra.Com's Answer #707223 by rothauserc(4718) $\"\"$ $\"About$

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Use the binomial probability formula
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\n" ); document.write( "Probability (P) (k events in n trials) = nCk * p^k * (1-p)^(n-k) where p is probability of event occurring, nCk = n! / (k! * (n-k)!)
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\n" ); document.write( "p = 0.15, n = 10
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\n" ); document.write( "a) P(x=2) = 10C2 * (0.15)^2 * (1-0.15)^(10-2) = 0.276 approximately 0.28
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\n" ); document.write( "b) P(x>=1) = 1 - P(x=0) = 1 - 0.20 = 0.80
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\n" ); document.write( "c) I assume by EX you mean E(X)
\n" ); document.write( "E(X) = np = 10 ^ 0.15 = 1.5
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\n" ); document.write( "d) Var(X) = np(1−p) = 10 * (0.15) * (1-0.15) = 1.275
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\n" ); document.write( "e) standard deviation of X = square root(1.275) = 1.1292
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