document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199130>Question 1199130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x	P(x)<BR>\n" );
document.write( "0	0.05<BR>\n" );
document.write( "1	0.2<BR>\n" );
document.write( "2	0.15<BR>\n" );
document.write( "3	0.6\r<BR>\n" );
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document.write( "Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.\r<BR>\n" );
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document.write( "I have attempted to multiply each x value by its corresponding P(x) value, and then added those values together. I got 1.97 as an answer, and it was incorrect. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844303 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=844303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You made an error somewhere when calculating the 1.97\r<BR>\n" );
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document.write( "The sum of the x*p(x) values is the mean.<BR>\n" );
document.write( "Refer to the table below to see that the mean should be mu = 2.3 instead of 1.97<BR>\n" );
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document.write( "<tr><TD >x</TD><TD >p(x)</TD><TD >x*p(x)</TD><TD >(x-mu)^2*p(x)</TD></tr><tr><TD >0</TD><TD >0.05</TD><TD >0</TD><TD >0.2645</TD></tr><tr><TD >1</TD><TD >0.2</TD><TD >0.2</TD><TD >0.338</TD></tr><tr><TD >2</TD><TD >0.15</TD><TD >0.3</TD><TD >0.0135</TD></tr><tr><TD >3</TD><TD >0.6</TD><TD >1.8</TD><TD >0.294</TD></tr><tr><TD >Sum</TD><TD >1</TD><TD >2.3</TD><TD >0.91</TD></tr>\n" );
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document.write( "That value of mu is then used to calculate the column (x-mu)^2*p(x)<BR>\n" );
document.write( "The sum of those values is 0.91 which is the variance. This value is exact without any rounding done to it.\r<BR>\n" );
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document.write( "Apply the square root of the variance to get the standard deviation.\r<BR>\n" );
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document.write( "SD = standard deviation<BR>\n" );
document.write( "SD = sqrt(variance)<BR>\n" );
document.write( "SD = sqrt(0.91)<BR>\n" );
document.write( "SD = 0.953939 approximately<BR>\n" );
document.write( "SD = 0.95\r<BR>\n" );
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document.write( "Various online calculators can be used to verify this result.<BR>\n" );
document.write( "Here is one such calculator<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.mathportal.org/calculators/statistics-calculator/probability-distributions-calculator.php\">https://www.mathportal.org/calculators/statistics-calculator/probability-distributions-calculator.php</a>\r<BR>\n" );
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document.write( "More practice with a similar question<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1206570.html\">https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1206570.html</a><BR>\n" );
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