document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199365>Question 1199365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! Good morning!\r<BR>\n" );
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document.write( "I'm doing some binomial distribution problems and I got stuck in this one, I managed to solve a, b and c but I don't know how to solve d.\r<BR>\n" );
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document.write( "66% of all students at a college still need to take another math class. If 34 students are randomly selected, find the probability that\r<BR>\n" );
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document.write( "a. Exactly 20 of them need to take another math class. <BR>\n" );
document.write( "0.09445\r<BR>\n" );
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document.write( "b. At most 21 of them need to take another math class. <BR>\n" );
document.write( "0.36062\r<BR>\n" );
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document.write( "c. At least 22 of them need to take another math class. <BR>\n" );
document.write( "0.63938\r<BR>\n" );
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document.write( "d. Between 22 and 28 (including 22 and 28) of them need to take another math class.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833219 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52797)</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=833219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hello! Good morning!<BR>\n" );
document.write( "I'm doing some binomial distribution problems and I got stuck in this one, <BR>\n" );
document.write( "I managed to solve a, b and c but I don't know how to solve d.\r<BR>\n" );
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document.write( "66% of all students at a college still need to take another math class. <BR>\n" );
document.write( "If 34 students are randomly selected, find the probability that\r<BR>\n" );
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document.write( "a. Exactly 20 of them need to take another math class.<BR>\n" );
document.write( "0.09445\r<BR>\n" );
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document.write( "b. At most 21 of them need to take another math class.<BR>\n" );
document.write( "0.36062\r<BR>\n" );
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document.write( "c. At least 22 of them need to take another math class.<BR>\n" );
document.write( "0.63938\r<BR>\n" );
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document.write( "d. Between 22 and 28 (including 22 and 28) of them need to take another math class.<BR>\n" );
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document.write( "So, &nbsp;you just know that it is a typical &nbsp;Binomial distribution problem.\r<BR>\n" );
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document.write( "The number of trials is &nbsp;n= 34;  &nbsp;the number of successful trials is &nbsp;\"k\", <BR>\n" );
document.write( "    different in different questions;\r<BR>\n" );
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document.write( "The probability of success of each individual trial is &nbsp;p= 0.66.\r<BR>\n" );
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document.write( "You may use an appropriate online &nbsp;(free of charge) &nbsp;calculator at this web-site \r<BR>\n" );
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document.write( "https://stattrek.com/online-calculator/binomial.aspx\r<BR>\n" );
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document.write( "It provides nice instructions  and  a convenient input and output for all relevant options/cases.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  P = P(n=34; k=20; p=0.66) = 0.09445.          You just know it . . . \r\n" );
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document.write( "(b)  P = P(n=34; k<=21; p=0.66) = 0.36062.         You just know it . . . \r\n" );
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document.write( "(c)  P = P(n=34; k>=22; p=0.66) = 0.63938.         You just know it . . . \r\n" );
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document.write( "(d)  P = P(n=34; k<=28; p=0.66) - P(n=34; k<=21; p=0.66)   <<<---===  you calculate the needed probability \r\n" );
document.write( "                                                                      as this DIFFERENCE of standard cumulative probabilities\r\n" );
document.write( "                                                                      using the standard functions\r\n" );
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document.write( "       = use the referenced calculator = 0.9895 - 0.36062 = 0.6289  (rounded).    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved and explained.\r<BR>\n" );
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document.write( "The major lesson to learn from my post is that the probability &nbsp;(d) &nbsp;is the difference of the appropriate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28CUMULATIVE%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28CUMULATIVE%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;probabilities, &nbsp;which you can calculate using the standard functions.\r<BR>\n" );
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document.write( "Which tool you will use - online calculator or your hand calculator - is just the secondary matter,\r<BR>\n" );
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document.write( "while the first row matter is to know &nbsp;WHAT &nbsp;to do.\r<BR>\n" );
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document.write( "Happy learning &nbsp;(&nbsp;!&nbsp;)\r<BR>\n" );
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document.write( "//////////////////\r<BR>\n" );
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document.write( "At this site, &nbsp;there are several lessons where many similar problems were solved and presented in all details\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> \r<BR>\n" );
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document.write( "Look into these lessons.\r<BR>\n" );
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document.write( "After reading/learning from these lessons, &nbsp;you will be able to solve such problems on your own, which is your \r<BR>\n" );
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document.write( "PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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