document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939927>Question 939927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose 10% of the population is left-handed. What’s the probability of<BR>\n" );
document.write( "seeing at most three left-handed students in a class of size 30?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572829 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   <BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "Assume class is a random sample with respect to left-handedness.<BR>\n" );
document.write( "population is 10% left-handed, i.e. probability p=0.10 is constant.<BR>\n" );
document.write( "The number of steps of the experiment is known, n=30.<BR>\n" );
document.write( "Each step is a Bernoulli experiment, i.e. with one of two possible outcomes.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Under these conditions, the binomial distribution applies.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Let P(X=r) be the probability of having r successes, then <BR>\n" );
document.write( "P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)<BR>\n" );
document.write( "where <BR>\n" );
document.write( "P(X=r) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Cr%29%2Ap%5Er%2A%281-p%29%5E%28n-r%29 ALIGN=MIDDLE  ALT=\"C%28n%2Cr%29%2Ap%5Er%2A%281-p%29%5E%28n-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C(n,r) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-r%29%21%2Ar%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-r%29%21%2Ar%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is combination of r objects out of n<BR>\n" );
document.write( "n = 30 = number steps of experiment<BR>\n" );
document.write( "p = 0.1 = probability of success (left-handed)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2830%2C0%29%2A0.1%5E0%2A%280.9%29%5E%2830%29+%2B+C%2830%2C1%29%2A0.1%5E1%2A%280.9%29%5E%2829%29+%2B+C%2830%2C2%29%2A2.1%5E0%2A%280.9%29%5E%2828%29+%2B+C%2830%2C3%29%2A0.1%5E3%2A%280.9%29%5E%2827%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=0.0424+%2B+0.1413+%2B+0.2277+%2B+0.2361 ALIGN=MIDDLE  ALT=\"0.0424+%2B+0.1413+%2B+0.2277+%2B+0.2361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6474 ALIGN=MIDDLE  ALT=\"0.6474\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "Answer: the probability of seeing up to 3 left-handed students is 0.6474\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );