Let X ~ Bin(9, 0.42) Calculate the standard deviation of X correct to 2dp.
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The formula for the standard deviation of a binomial distribution is: σ = √(npq) where n is the number of trials, p is the probability of success, and q is the probability of failure (q = 1 - p). Show more…
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Find the standard deviation. $$\begin{array}{|c|c|c|c|}\hline x & {P(x)} & {x^{*} P(x)} & {(x-\mu)^{2} P(x)} \\ \hline 2 & {0.1} & {2(0.1)=0.2} & {(2-5.4)^{2}(0.1)=1.156} \\ \hline 4 & {0.3} & {4(0.3)=1.2} & {(4-5.4)^{2}(0.3)=0.588} \\ \hline 6 & {0.4} & {6(0.4)=2.4} & {(6-5.4)^{2}(0.4)=0.144} \\ \hline 8 & {0.2} & {8(0.2)=1.6} & {(8-5.4)^{2}(0.2)=1.352} \\ \hline \end{array}$$
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