document.write( "Question 1194599: Let X be a random variable having a binomial distribution with parameters n=25 and p=0.2 evaluate P[𝑋<𝜇𝑥−2𝜎𝑥] \n" ); document.write( "

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Let X be a random variable having a binomial distribution with parameters n=25 and p=0.2 evaluate P[𝑋<𝜇𝑥−2𝜎𝑥]\r
\n" ); document.write( "\n" ); document.write( "Solution:
\n" ); document.write( "The mean and variance of Binomial(n, p) are E(X) =np and Var(X) = np(1-p), respectively.\r
\n" ); document.write( "\n" ); document.write( "The mean of X is E(X)= np = 25(0.2) = 5 and the variance is Var(X)= np(1-p) = 25(0.2)(0.8) = 4.
\n" ); document.write( "The standard deviation of X is the square root of the variance which is 2.
\n" ); document.write( "We want to find P[𝑋<𝜇𝑥−2𝜎𝑥] = P[𝑋< 5 - 2(2)] = P(X < 1) = P(X = 0) = $\"0.8%5E25\"$ = 0.003777893\r
\n" ); document.write( "\n" ); document.write( "If you have clarifications, just email me (reviewermath yahoo). I can tutor you on the whiteboard.\r
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