Question 1118194
Use the Binomial Probability Distribution Formula
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Probability (P) (k successes in n trials) = nCk * p^(k) * (1-p)^(n-k), where nCk = n! / (k! * (n-k)!)
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For these problems n=8 and p=0.16
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a) P (k=0) = 8C0 * (0.16)^0 * (1-0.16)^(8-0) = 0.2479
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b) P (k=1) = 8C1 * (0.16)^1 * (1-0.16)^(8-1) = 0.3777
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c) P (k=2) = 8C2 * (0.16)^2 * (1-0.16)^(8-2) = 0.2518
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d) P (k<3) = P(k=0) +P(k=1) +P(k=2) = 0.2479 +0.3777 +0.2518 = 0.8774
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e. Compute the mean and standard deviation of this probability distribution
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mean = 8 * 0.16 = 1.28
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standard deviation = square root(n * p * (1-p)) = square root(8 * 0.16 * (1-0.16)) = 1.0369
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