document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=406695>Question 406695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The numbers of people waiting in the emergency clinic of a small health care facility were randomly counted thirty-five times. Using the data below and the appropriate formula, set up a 95% confidence interval for the mean number of people waiting in emergency.<BR>\n" );
document.write( "11	12	13	13	14	14	14<BR>\n" );
document.write( "15	17	16	16	17	17	16<BR>\n" );
document.write( "15	15	18	19	16	16	18<BR>\n" );
document.write( "17	17	18	17	16	16	16<BR>\n" );
document.write( "15	9	10	18	14	11	9<BR>\n" );
document.write( "(where x and s are calculated from the sample data, n = 35 and z = 1.96)<BR>\n" );
document.write( "Remember to show all your work and round your final answer to the nearest whole number.\r<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 #286924 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the mean :\r<BR>\n" );
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document.write( "11 12 13 13 14 14 14........91<BR>\n" );
document.write( "15 17 16 16 17 17 16..........114<BR>\n" );
document.write( "15 15 18 19 16 16 18..........117<BR>\n" );
document.write( "17 17 18 17 16 16 16..........117<BR>\n" );
document.write( "15 9 10 18 14 11 9..................86\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2891%2B114%2B117%2B117%2B86%29%2F35=+525%2F35=15 ALIGN=MIDDLE  ALT=\"%2891%2B114%2B117%2B117%2B86%29%2F35=+525%2F35=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >......the mean is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=interval+ ALIGN=MIDDLE  ALT=\"interval+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is\r<BR>\n" );
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document.write( "Find the standard deviation of  using this formula first:\r<BR>\n" );
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document.write( "subtract the mean individually from each of the numbers in the question and square the result.<BR>\n" );
document.write( "x               11       12        13       13       14       14        14        <BR>\n" );
document.write( "(x - x)²     16         9           4       4           1         1           1..........36\r<BR>\n" );
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document.write( "x               15       17        16       16       17       17        16        <BR>\n" );
document.write( "(15 - x)²     0         4           1        4         4         4          1.............18\r<BR>\n" );
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document.write( " x   	    15 	15	18	 19	 16	 16 	18<BR>\n" );
document.write( "(15 - x)²     0	 0  	  9	   16        1          1         9.............36\r<BR>\n" );
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document.write( "x   	    17 	17	18	 17	 16	 16 	16<BR>\n" );
document.write( "(15 - x)²     4	 4  	  9	  4          1          1         1..................24\r<BR>\n" );
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document.write( "x   	    15 	 9	10	 18	 14	 11 	9<BR>\n" );
document.write( "(15 - x)²     0	 36  	  25	  9          1          16      36............123<BR>\n" );
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document.write( "                                                                                                     237<BR>\n" );
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document.write( "Now add up these results (this is the 'sigma' in the formula): 237\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lower_case_sigma+=+sqrt%28uper_case_sigma%28x+-+x%29%5E2%2F%28n-1%29%29+%0D%0A%0D%0A%7B%7B%7Bn=35 ALIGN=MIDDLE   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=lower_case_sigma+=+sqrt%28237%2F34%29 ALIGN=MIDDLE  ALT=\"lower_case_sigma+=+sqrt%28237%2F34%29\"   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=lower_case_sigma+=+sqrt%286.9705882352941176470588235294118%29 ALIGN=MIDDLE  ALT=\"lower_case_sigma+=+sqrt%286.9705882352941176470588235294118%29\"   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=lower_case_sigma+=+%282.6401871591412071041056987587526%29 ALIGN=MIDDLE  ALT=\"lower_case_sigma+=+%282.6401871591412071041056987587526%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the standard deviation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.6401871591412071041056987587526%29 ALIGN=MIDDLE  ALT=\"%282.6401871591412071041056987587526%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	 		\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B-zs%2Fsqrt%28n%29 ALIGN=MIDDLE  ALT=\"x+%2B-zs%2Fsqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "= 15 +-(1.96(2.6401871591412071041056987587526))/sqrt(35)\r<BR>\n" );
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document.write( "= 15 +-( 5.1747668319167659240471695671539)=15+-5.18\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+%2B5.18+=20.17 ALIGN=MIDDLE  ALT=\"15+%2B5.18+=20.17\"   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=15+-5.18+=+9.82 ALIGN=MIDDLE  ALT=\"15+-5.18+=+9.82\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the interval is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.82%3Cthe_+interval%3C20.17 ALIGN=MIDDLE  ALT=\"9.82%3Cthe_+interval%3C20.17\"   DISABLED_style= \"max-width:90%; height:auto;\" >....in average:14.995\r<BR>\n" );
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