document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154331>Question 1154331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Susan keeps track of the number of tickets sold for each play presented at The Community Theater. The mean of her data is 117, and the standard deviation is 47. Within how many standard deviations of the mean do all the values fall? Data: 59, 143, 80, 69, 176, 86, 160, 65, 152, 184 *<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776779 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=776779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Original set = {59, 143, 80, 69, 176, 86, 160, 65, 152, 184}<BR>\n" );
document.write( "Sorted set = {59, 65, 69, 80, 86, 143, 152, 160, 176, 184}<BR>\n" );
document.write( "min = 59 and max = 184\r<BR>\n" );
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document.write( "mu = mean = 117<BR>\n" );
document.write( "sigma = standard deviation = 47\r<BR>\n" );
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document.write( "1 standard deviation from the mean<BR>\n" );
document.write( "L = lower bound = mu - 1*sigma = 117-1*47 = 70<BR>\n" );
document.write( "U = upper bound = mu + 1*sigma = 117+1*47 = 164\r<BR>\n" );
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document.write( "Ask yourself: Do all of the data values fall within the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70+%3C=+x+%3C=+164 ALIGN=MIDDLE  ALT=\"70+%3C=+x+%3C=+164\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%3C=+x+%3C=+U ALIGN=MIDDLE  ALT=\"L+%3C=+x+%3C=+U\"   DISABLED_style= \"max-width:90%; height:auto;\" >)? The answer is 'no' because 59, 65, 69, 176, and 184 are outside this range.\r<BR>\n" );
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document.write( "2 standard deviations from the mean<BR>\n" );
document.write( "L = lower bound = mu - 2*sigma = 117-2*47 = 23<BR>\n" );
document.write( "U = upper bound = mu + 2*sigma = 117+2*47 = 211\r<BR>\n" );
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document.write( "The interval is now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23+%3C=+x+%3C=+211 ALIGN=MIDDLE  ALT=\"23+%3C=+x+%3C=+211\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Ask a similar question: Do all of the data values fall within the range <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23+%3C=+x+%3C=+211 ALIGN=MIDDLE  ALT=\"23+%3C=+x+%3C=+211\"   DISABLED_style= \"max-width:90%; height:auto;\" >? The answer is 'yes'. This is because L = 23 is smaller than the min = 59, while U = 211 is larger than the max = 184.\r<BR>\n" );
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document.write( "Final Answer: <font size=4 color=red>2 standard deviations</font><BR>\n" );
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