document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207329>Question 1207329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays. (a) Use Excel or MegaStat to sort and standardize the data. (b) Based on the Empirical Rule, are there outliers? Unusual data values? (c) Compare the percent of observations that lie within 1 and 2 standard deviations of the mean with a normal distribution. What is your conclusion? CitiBank<BR>\n" );
document.write( "25 37 23 26 30 40 25 26 39 32 21 26 19 27 32 25 18 26 34 18 31 35 21 33 33 9 16 32 35 42 15 24<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 #845148 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "here is a reference on the empirical rule.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://corporatefinanceinstitute.com/resources/data-science/empirical-rule/#:~:text=Within%20the%20first%20standard%20deviation,exist%20in%20almost%20every%20dataset)\" target = \"_blank\">https://corporatefinanceinstitute.com/resources/data-science/empirical-rule/#:~:text=Within%20the%20first%20standard%20deviation,exist%20in%20almost%20every%20dataset)</a>\r<BR>\n" );
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document.write( "for this particular problem, i'm assumig the data is from the population.\r<BR>\n" );
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document.write( "here are some descriptive statistics from the calculator at <a  rel=nofollow HREF= \"http://www.alcula.com/calculators/statistics/dispersion/#gsc.tab=0\" target = \"_blank\">http://www.alcula.com/calculators/statistics/dispersion/#gsc.tab=0</a>\r<BR>\n" );
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document.write( "the mean is equal to 27.34375<BR>\n" );
document.write( "the standard deviation is equal to 7.728233 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "the empirical rule states that 99.7% of the data lies within 3 standard deviations of the mean.<BR>\n" );
document.write( "it also states that any data beyond this range is considered an outlier.\r<BR>\n" );
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document.write( "the critical scores for 99.7% of the data would be a minimum of 4.041 and a maximum of 50.646.<BR>\n" );
document.write( "the smallest data is 9 and the largest date is 42.<BR>\n" );
document.write( "therefore, there are no outliers according to the empirical rule.\r<BR>\n" );
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document.write( "the data input was sorted by the calculator, so it was easy to see the minimum and maximum values.\r<BR>\n" );
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document.write( "the empirical rule states that 95% of the data falls within 2 standard deviations of the mean.\r<BR>\n" );
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document.write( "the critical scores for 95% of the data would be a minimum of 11.954 and a maximum of 42.733.\r<BR>\n" );
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document.write( "31 elements of data fall within those extremes.<BR>\n" );
document.write( "that's approximately 31/32 = 96.875%.<BR>\n" );
document.write( "that's within 2% of 95% which is pretty close, so the data app[ears to be consistent with the rules for a normal distribution.\r<BR>\n" );
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document.write( "here are the statistics from the normal distribution calculator, using the mean and standard deviation from the data.\r<BR>\n" );
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