document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767788>Question 767788</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability that an individual is left-handed is .20. Let the random variable X bethe number of left-handers in a class of 20 students. Assuming the random variable X has a binomial distribution:\r<BR>\n" );
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document.write( "a) What is the probability distribution, P(X) of the random variable X.<BR>\n" );
document.write( "b) What is the mean number (expected value) of left-handers in the class?<BR>\n" );
document.write( "c) What is the probability that there is exactly 5 left-handers in the class?<BR>\n" );
document.write( "d) What is the probability that the number of left-handers are between 6 and 10 inclusively (including 6 and 10)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467873 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability that an individual is left-handed is .20. Let the random variable X bethe number of left-handers in a class of 20 students. Assuming the random variable X has a binomial distribution:<BR>\n" );
document.write( "a) What is the probability distribution, P(X) of the random variable X.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%28X+=+x%29+=+%28matrix%282%2C1%2C20%2Cx%29%29%280.2%5Ex%29%280.8%5E%2820-x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > for x = 0,1,2,...,20<BR>\n" );
document.write( "b) What is the mean number (expected value) of left-handers in the class?<BR>\n" );
document.write( "Mean, E(X) = np = 20(0.2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284%29 ALIGN=MIDDLE  ALT=\"highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) What is the probability that there is exactly 5 left-handers in the class?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+=+5%29+=+%28matrix%282%2C1%2C20%2C5%29%29%280.2%5E5%29%280.8%5E15%29 ALIGN=MIDDLE  ALT=\"P%28X+=+5%29+=+%28matrix%282%2C1%2C20%2C5%29%29%280.2%5E5%29%280.8%5E15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.17456%29 ALIGN=MIDDLE  ALT=\"highlight%280.17456%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d) What is the probability that the number of left-handers are between 6 and 10 inclusively (including 6 and 10)?<BR>\n" );
document.write( "P(6 &#8804; X &#8804; 10) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28matrix%282%2C1%2C20%2Cx%29%29%280.2%5Ex%29%280.8%5E%2820-x%29%29%2Cx+=+6%2C10%29 ALIGN=MIDDLE  ALT=\"sum%28%28matrix%282%2C1%2C20%2Cx%29%29%280.2%5Ex%29%280.8%5E%2820-x%29%29%2Cx+=+6%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.19523%29 ALIGN=MIDDLE  ALT=\"highlight%280.19523%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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