document.write( "Question 165388: Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of getting 251 heads or less. \n" ); document.write( "
Algebra.Com's Answer #121998 by gonzo(654)\"\" \"About 
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using normal curve approximation:
\n" ); document.write( "n = 500
\n" ); document.write( "p = .5
\n" ); document.write( "x = 251
\n" ); document.write( "s (standard deviation) = sqrt(500*.5*.5) = sqrt(125) = 11.18033989
\n" ); document.write( "z = (x-n*p)/s
\n" ); document.write( "n*p = 500 * .5 = 250
\n" ); document.write( "x = 251
\n" ); document.write( "x-n*p = 251-250 = 1
\n" ); document.write( "(x-n*p)/s = 1/11.18033989 = .089442719
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\n" ); document.write( "using the online z table evaluator, probability of getting 251 heads or less is
\n" ); document.write( ".535635
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\n" ); document.write( "that would be the area under the curve for values less than .089442719 with the mean = 0 and the standard deviation = 1
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\n" ); document.write( "since n*p = mean of normal distribution, you will get the same answer if you plug in a mean of 250 and an s (standard deviation) of 11.18033989 and you ask for the area under the curve for all values of x less than 251.
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\n" ); document.write( "z table evaluator can be found at:
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\n" ); document.write( "http://davidmlane.com/hyperstat/z_table.html
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