document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169655>Question 1169655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 67% of children in a school do not have cavities. Let x be the number of children in a random sample of 70 children selected from this school who do not have cavities. The mean and standard deviation of the probability distribution of x, rounded to two decimal places, are?\r<BR>\n" );
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document.write( "Just looking for clarification,<BR>\n" );
document.write( "Mean is 67<BR>\n" );
document.write( "The standard deviation is 8.1853\r<BR>\n" );
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document.write( "If not I'm very confused then :( </SPAN>\n" );
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document.write( "67% of the children do not have cavities<BR>\n" );
document.write( "p = 0.67 is the probability of selecting a child who does not cavities.\r<BR>\n" );
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document.write( "n = 70 is the sample size\r<BR>\n" );
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document.write( "mu = mean<BR>\n" );
document.write( "sigma = standard deviation\r<BR>\n" );
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document.write( "For a binomial distribution it has the following formulas<BR>\n" );
document.write( "mu = n*p <BR>\n" );
document.write( "sigma = sqrt( n*p*(1-p) )\r<BR>\n" );
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document.write( "Let's first find the mean<BR>\n" );
document.write( "mu = n*p <BR>\n" );
document.write( "mu = 70*0.67<BR>\n" );
document.write( "mu = 46.9<BR>\n" );
document.write( "The mean is exactly 46.9\r<BR>\n" );
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document.write( "Now the standard deviation<BR>\n" );
document.write( "sigma = sqrt( n*p*(1-p) )<BR>\n" );
document.write( "sigma = sqrt( 70*0.67*(1-0.67) )<BR>\n" );
document.write( "sigma = 3.93408184968233<BR>\n" );
document.write( "sigma = 3.93<BR>\n" );
document.write( "The standard deviation is approximately 3.93\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "mean = 46.9<BR>\n" );
document.write( "standard deviation = 3.93<BR>\n" );
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