document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036225>Question 1036225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let the random variable x represent the number of girls in a family with three children. The probability of a child being a girls in 0.36. Construct a table describing the probability distribution, then find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650908 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the number of girls in a family with three children. Then the r.v. has pmf<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+%28matrix%282%2C1%2C3%2Cx%29%29%2A0.64%5E%283-x%29%2A0.36%5Ex+=+0.262144 ALIGN=MIDDLE  ALT=\"p%28x%29+=+%28matrix%282%2C1%2C3%2Cx%29%29%2A0.64%5E%283-x%29%2A0.36%5Ex+=+0.262144\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where x = 0,1,2,3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%280%29+=+%28matrix%282%2C1%2C3%2C0%29%29%2A0.64%5E3%2A0.36%5E0+=+0.262144 ALIGN=MIDDLE  ALT=\"p%280%29+=+%28matrix%282%2C1%2C3%2C0%29%29%2A0.64%5E3%2A0.36%5E0+=+0.262144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281%29+=+%28matrix%282%2C1%2C3%2C1%29%29%2A0.64%5E2%2A0.36%5E1+=+0.442368 ALIGN=MIDDLE  ALT=\"p%281%29+=+%28matrix%282%2C1%2C3%2C1%29%29%2A0.64%5E2%2A0.36%5E1+=+0.442368\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%282%29+=+%28matrix%282%2C1%2C3%2C2%29%29%2A0.64%5E1%2A0.36%5E2+=+0.248832 ALIGN=MIDDLE  ALT=\"p%282%29+=+%28matrix%282%2C1%2C3%2C2%29%29%2A0.64%5E1%2A0.36%5E2+=+0.248832\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%283%29+=+%28matrix%282%2C1%2C3%2C3%29%29%2A0.64%5E0%2A0.36%5E3+=+0.046656 ALIGN=MIDDLE  ALT=\"p%283%29+=+%28matrix%282%2C1%2C3%2C3%29%29%2A0.64%5E0%2A0.36%5E3+=+0.046656\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Mean = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+np+=+3%2A0.36+=+1.08 ALIGN=MIDDLE  ALT=\"mu+=+np+=+3%2A0.36+=+1.08\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Or practically, the mean number of girls in 3 children is 1, given the conditions.)\r<BR>\n" );
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document.write( "==>Standard deviation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+sqrt%28npq%29+=+sqrt%283%2A0.36%2A0.64%29+=+0.83 ALIGN=MIDDLE  ALT=\"sigma+=+sqrt%28npq%29+=+sqrt%283%2A0.36%2A0.64%29+=+0.83\"   DISABLED_style= \"max-width:90%; height:auto;\" > to two significant figures.\r<BR>\n" );
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document.write( "Under the given condition (p = 0.36), it is unusual for a family of 3 children to consist of 3 girls (chance is only 4.7%.)\r<BR>\n" );
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