document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189291>Question 1189291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let x be the number of heads which occur when a coin is tossed 100 times and Y be the number of ones which occur when a die is rolled 300 times.\r<BR>\n" );
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document.write( "Find P(45 < X < 55) and P(45 < Y < 55) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820621 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53765)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Let x be the number of heads which occur when a coin is tossed 100 times <BR>\n" );
document.write( "and Y be the number of ones which occur when a die is rolled 300 times.<BR>\n" );
document.write( "Find P(45 < X < 55) and P(45 < Y < 55)<BR>\n" );
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document.write( "Both are typical binomial distributions.\r<BR>\n" );
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document.write( "Since the number of trials is comparatively large, &nbsp;it is recommended to use <BR>\n" );
document.write( "the normal approximation to binomial distribution.\r<BR>\n" );
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document.write( "Go to web-site  https://mathcracker.com/normal-approximation-binomial-distribution\r<BR>\n" );
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document.write( "and find there online calculator specialized for such calculations.\r<BR>\n" );
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document.write( "It has perfect description, &nbsp;clear instructions and simple and convenient input.\r<BR>\n" );
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document.write( "The output includes full theory/explanations with detailed step-by-step calculations shown,<BR>\n" );
document.write( "and with every step commented.\r<BR>\n" );
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document.write( "It also provides graphical illustration of normal curve.\r<BR>\n" );
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document.write( "The calculator gives  &nbsp;&nbsp;P(45 < X < 55) = 0.6319    &nbsp;&nbsp;&nbsp;&nbsp;(with p = 0.5)\r<BR>\n" );
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document.write( "                    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;P(45 < Y < 55) = 0.5143    &nbsp;&nbsp;&nbsp;&nbsp;(with p = 1/6 = 0.16666)\r<BR>\n" );
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document.write( "In parallel with computing, &nbsp;learn the relevant theory from this web-site.\r<BR>\n" );
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document.write( "//////////\r<BR>\n" );
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document.write( "Dear Edwin,\r<BR>\n" );
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document.write( "you can see some difference between my answer and your calculations.\r<BR>\n" );
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document.write( "I don't know precisely, what is the source of this difference.\r<BR>\n" );
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document.write( "I only know that they in the site refer to some \"continuity correction factor\",<BR>\n" );
document.write( "which they do apply, while you do not.\r<BR>\n" );
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document.write( "I am not a specialist in it.\r<BR>\n" );
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document.write( "But I think that it would be interesting to learn in some way which methodology is correct.\r<BR>\n" );
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document.write( "Yesterday, very similar problem came to the forum and was solved by @Boreal under this link\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1189215.html\r<BR>\n" );
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document.write( "@Boreal also applied this \"continuity correction factor\".\r<BR>\n" );
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document.write( "I performed similar calc with the solver for that condition, and obtained the same number/(answer) as @Boreal, with 4 decimal figures.\r<BR>\n" );
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document.write( "Please do not consider my post as an attempt to disprove or challenge your solution.\r<BR>\n" );
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document.write( "It is only my request to specialists to find the truth.\r<BR>\n" );
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document.write( "................ (written 1.5 hours later)\r<BR>\n" );
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document.write( "Edwin, &nbsp;I made several numerical experiments, &nbsp;and it seems to me that I found the source of discrepancy.  \r<BR>\n" );
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document.write( "normalcdf(45.5,54.5,50,5) = 0.6319, precisely as with the online calculator,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;where I assigned the lower and upper limits as 46 and 54.\r<BR>\n" );
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document.write( "normalcdf(45.5,54.5,50,6.454972244) = 0.5143, precisely as with the online calculator,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;where I assigned the lower and upper limits as 46 and 54.\r<BR>\n" );
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document.write( "So, &nbsp;it looks like my question is resolved, &nbsp;and the online calculator is correct.\r<BR>\n" );
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document.write( "The matter is in assigning upper and lower limits in the function &nbsp;normalcdf &nbsp;of pocket &nbsp;(physical) &nbsp;calculators.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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