document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74693>Question 74693</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131483161/algebrahomeworkh>Elementary Statistics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> In a recent survey, 66% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the police substation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53679 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a recent survey, 66% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the police substation.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "This is a binomial probability problem.<BR>\n" );
document.write( "The formula for that is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%28x%29=%28n%21%2F%28%28n-x%29%21x%21%29%29%2Ap%5Ex%2Aq%5E%28n-x%29%29 ALIGN=MIDDLE  ALT=\"highlight%28P%28x%29=%28n%21%2F%28%28n-x%29%21x%21%29%29%2Ap%5Ex%2Aq%5E%28n-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for x=0,1,2,...,n<BR>\n" );
document.write( "Where:<BR>\n" );
document.write( "n=number of trials<BR>\n" );
document.write( "x=number of successes among n trials<BR>\n" );
document.write( "p=probability of success in any one trial<BR>\n" );
document.write( "q=probability of failure in any one trial (q=1-p)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "! is a factorial symbol that denotes the product of descending numbers, like this:<BR>\n" );
document.write( "4!=4*3*2*1  If your in a statistics class you probably have a calculator with the ! symbol available some where.  For the TI 83 to TI 84, hit [MATH] arrow right>>> to PRB it's 4:!.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Some teachers allow you to shorten the formula to:<BR>\n" );
document.write( "P(x)=[n]C[r]*p^x*q^(n-x)<BR>\n" );
document.write( "r=x=number of successes among n trials.  <BR>\n" );
document.write( "All of the other symbols are the same as the first formula.  If you're one of those, then you should know how to do it with your calculator.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I'm going to show you with the first formula.<BR>\n" );
document.write( "p=66/100=.66<BR>\n" );
document.write( "q=1-p=1-.66=.34<BR>\n" );
document.write( "n=14<BR>\n" );
document.write( "x=11<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=%2814%21%2F%28%2814-11%29%2111%21%29%29%2A%28.66%29%5E%2811%29%2A%28.34%29%5E%2814-11%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=%2814%21%2F%283%21%2A11%21%29%29%2A%28.66%29%5E11%2A%28.34%29%5E3 ALIGN=MIDDLE  ALT=\"P%2811%29=%2814%21%2F%283%21%2A11%21%29%29%2A%28.66%29%5E11%2A%28.34%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=%28%2814%2A13%2A12%2A11%21%29%2F%283%2A2%2A1%2A11%21%29%29%2A%28.66%29%5E11%2A%28.34%29%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=%28%2814%2A13%2A12%2Across%2811%21%29%29%2F%286%2Across%2811%21%29%29%29%2A%28.0103510234%29%28.039304%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=%28%2814%2A13%2A2%2Across%286%29%29%2Fcross%286%29%29%2A%28.0103510234%29%28.039304%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=%2814%2A13%2A2%29%28.0103510234%29%28.039304%29 ALIGN=MIDDLE  ALT=\"P%2811%29=%2814%2A13%2A2%29%28.0103510234%29%28.039304%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2811%29=.148088531 ALIGN=MIDDLE  ALT=\"P%2811%29=.148088531\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Round to whatever your teacher wants, most don't require more than 4 decimal spots.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%2811%29=.1481%29 ALIGN=MIDDLE  ALT=\"highlight%28P%2811%29=.1481%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "I don't know how much work your teacher needs to see.  If they only want an answer, then....<BR>\n" );
document.write( "If you have a TI 83 to TI 84, these can be done by following these steps:<BR>\n" );
document.write( "[2nd] [VARS] arrow down to 0:binompdf [ENTER]<BR>\n" );
document.write( "type in [n] [,] [p] [,] [x] [)] [ENTER]<BR>\n" );
document.write( "In this case it will look like binompdf(14,.66,11)=.1480885312<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Look the instructions up for the calculator that you're using if it's not a TI 83 or 84.<BR>\n" );
document.write( "Happy Calculating!!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );