document.write( "Question 1075970: Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
\n" ); document.write( "n=58, p=0.3, and X=24 \n" ); document.write( "
Algebra.Com's Answer #690640 by stanbon(75887)\"\" \"About 
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Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
\n" ); document.write( "n=58, p=0.3, and X=24
\n" ); document.write( "p*n = 0.3*58 > 5
\n" ); document.write( "q*n = 0.7*58 > 5
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\n" ); document.write( "P(x = 24) = P(23.5 < x < 24.5)
\n" ); document.write( "np = 0.3*58 = 17.4
\n" ); document.write( "sqrt(npq) = sqrt(17.4*0.7) = 3.49
\n" ); document.write( "--
\n" ); document.write( "z(23.5) = (23.5-17.4)/3.49 = 1.748
\n" ); document.write( "z(24.5) = (24.5-17.4)/3.49 = 2.034
\n" ); document.write( "---
\n" ); document.write( "P(x = 24) = P(1.748< z < 2.034) = 0.0193 (normal approximation)
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\n" ); document.write( "P(x = 24) = 58C24(0.3^24)(0.7^34) = 0.0196
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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