document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178817>Question 1178817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A travel agency call centre wants to know the average number of calls received per<BR>\n" );
document.write( "day by its call centre. A random sample of 21 days is selected and the sample mean<BR>\n" );
document.write( "number of calls received was found to be 166.2 with a sample standard deviation of<BR>\n" );
document.write( "22.8 calls. Assume that calls received daily are normally distributed.<BR>\n" );
document.write( "(a) Calculate a 95% confidence interval for the mean number of daily calls received<BR>\n" );
document.write( "by the call centre. Interpret the findings (3 marks).<BR>\n" );
document.write( "(b) Find a 99% confidence interval for the mean number of daily calls received by<BR>\n" );
document.write( "the call centre (3 marks).<BR>\n" );
document.write( "(c) Compare the findings of (a) and (b) and explain the reason for the difference (2<BR>\n" );
document.write( "marks).<BR>\n" );
document.write( "(d) Estimate, with 95% confidence, the total number of calls received over a 30-day<BR>\n" );
document.write( "period. Interpret the result  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850292 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1980)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You've presented the same problem again, and I've already provided a complete and detailed solution in my previous response. \r<BR>\n" );
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document.write( "To recap, here are the key findings:\r<BR>\n" );
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document.write( "**(a) 95% Confidence Interval:**\r<BR>\n" );
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document.write( "* **Interval:** Approximately 155.823 to 176.577 calls.<BR>\n" );
document.write( "* **Interpretation:** We are 95% confident that the true average number of daily calls is within this range.\r<BR>\n" );
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document.write( "**(b) 99% Confidence Interval:**\r<BR>\n" );
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document.write( "* **Interval:** Approximately 152.050 to 180.350 calls.\r<BR>\n" );
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document.write( "**(c) Comparison:**\r<BR>\n" );
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document.write( "* The 99% interval is wider than the 95% interval.<BR>\n" );
document.write( "* This is because a higher confidence level requires a larger margin of error.\r<BR>\n" );
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document.write( "**(d) 95% Confidence Interval for 30 Days:**\r<BR>\n" );
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document.write( "* **Interval:** Approximately 4674.69 to 5297.31 calls.<BR>\n" );
document.write( "* **Interpretation:** We are 95% confident that the total calls over 30 days are within this range.\r<BR>\n" );
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document.write( "If you have any other questions or need further clarification on any specific part of the solution, please let me know!<BR>\n" );
document.write( " </SPAN>\n" );
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