document.write( "Question 620100: (A) Find the binomial probability P(x = 6), where n = 15 and p = 0.30.
\n" ); document.write( "(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
\n" ); document.write( "(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.
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Algebra.Com's Answer #389910 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
(A) Find the binomial probability P(x = 6), where n = 15 and p = 0.30.
\n" ); document.write( "P(x=6) = 15C6*0.3^6*0.7^9 = binompdf(15,0.3,6) = 0.1472
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\n" ); document.write( "\n" ); document.write( "(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
\n" ); document.write( "P(0<= x <=6) = binomcdf(15,0.3,6) = 0.8689
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\n" ); document.write( "\n" ); document.write( "(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.
\n" ); document.write( "mean = np = 15*0.3 = 4.5
\n" ); document.write( "std = sqrt(npq) = sqrt(4.5*0.7) = 1.7748
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\n" ); document.write( "P(x = 6) = P(5.5<= x <= 6.5)
\n" ); document.write( "z(5.5) = (5.5-4.5)/1.7748 = 0.5634
\n" ); document.write( "Z(6.5) = (6.5-4.5)/1.7748 = 1.1269
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\n" ); document.write( "Then approx P(x = 6) = P(0.5634< z < 1.1269) = 0.1567
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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