document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002049>Question 1002049</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You ask your graduate student to roll a die 10,000 times and record the results. Give the expected mean and standard deviation of the outcome. Part B: The die roll experiment is repeated (though with a different graduate student – for some reason your previous student went to work with a different advisor). However in this case, the die is weighted so that a 6 shows up 20% of the time and all remaining numbers show up 16% of the time. Now what is the mean and sd of 10,000 rolls? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619084 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in a proportion, the mean is equal to np and the standard deviation is equal to sqrt(npq)\r<BR>\n" );
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document.write( "p is the probability of success.<BR>\n" );
document.write( "q is the probability of failure.<BR>\n" );
document.write( "q = 1 minus p\r<BR>\n" );
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document.write( "in a fair dice, probability of getting a 6 is 1/6 and probability of not getting a 6 is 5/6.\r<BR>\n" );
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document.write( "you get p = 1/6 and q = 5/6.\r<BR>\n" );
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document.write( "with 10,000 rolls, mean is np = 10,000 * 1/6 = 10,000/6.\r<BR>\n" );
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document.write( "standard deviation is sqrt(n*p*q) = sqrt(10,000 * 1/6 * 5/6) = sqrt(50,000/36).\r<BR>\n" );
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document.write( "in decimal form rounded to 2 decimal places, you have mean = 1666.67 and standard deviaton = 37.27.\r<BR>\n" );
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document.write( "when p = .2, you get:\r<BR>\n" );
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document.write( "p = 1/5 and q = 4/5.\r<BR>\n" );
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document.write( "n is still 10,000.\r<BR>\n" );
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document.write( "mean =  np = 10,000 * 1/5 = 10,000/5.\r<BR>\n" );
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document.write( "standard deviation = sqrt(npq) = sqrt(10,000 * 1/5 * 4/5) = sqrt(40,000/25)\r<BR>\n" );
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document.write( "in decimal form rounded to 2 decimal places, you have mean = 2000 and standard deviation = 40.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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