document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=898088>Question 898088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem:\r<BR>\n" );
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document.write( "The number of passengers carried by a coastal shipping company has a normally distribution with mean 121.3 and standard deviation of 7.5.<BR>\n" );
document.write( "   a) find the 25th percentile of passengers carried by the ship.<BR>\n" );
document.write( "   b) find a 95 percent confidence interval for the number of passengers  carried by the ship. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #544563 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=544563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 121.3<BR>\n" );
document.write( "standard deviation = 7.5\r<BR>\n" );
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document.write( "25th percentile means that 25% of the area under the normal distribution curve is to the left of the z-score indicated.\r<BR>\n" );
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document.write( "use a z-score calculator to find that the z-score for that is equal to -.6744897...\r<BR>\n" );
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document.write( "since z-score = (raw score minus mean) / standard deviation, you get:\r<BR>\n" );
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document.write( "-.6744897... = (x - 121.3) / 7.5\r<BR>\n" );
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document.write( "solve for x to get x = 116.2423269... which you can round to 116.2.\r<BR>\n" );
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document.write( "95th percent confidence interval is calculated as follows:\r<BR>\n" );
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document.write( "two sided confidence interval alpha = (100% - 95%) / 200 = .025\r<BR>\n" );
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document.write( "the z-scores correspond to that will be a z-score that has 2.5% of the area under the normal distribution curve to the left of it, and a z-score that has 97.5% of the area under the normal distribution curve to the left of it.\r<BR>\n" );
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document.write( "to find the confidence interval, you then subtract the smaller area from the bigger area to get the area in between.\r<BR>\n" );
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document.write( "the z-score for an area of 2.5% is equal to -1.959963...<BR>\n" );
document.write( "the z-score for an area of 97.5% is equal to 1.959963...\r<BR>\n" );
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document.write( "the area in between is equal to 97.5 - 2.5 = 905% of the area unde rthe normal distribution curve.\r<BR>\n" );
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document.write( "you need to translate the z-scores to raw score.\r<BR>\n" );
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document.write( "a z-score of -9.959963... will yield a raw score as follows:\r<BR>\n" );
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document.write( "-9.959963... = (x - 121.3) / 7.5 <BR>\n" );
document.write( "solve for x to get x = 106.6002701...\r<BR>\n" );
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document.write( "a z-score of 9.959963... will yield a raw score as follows:\r<BR>\n" );
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document.write( "9.959963... = (x - 121.3) / 7.5<BR>\n" );
document.write( "solve for x to get x = 135.9997299...\r<BR>\n" );
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document.write( "round these to the nearest one decimal place and you get:\r<BR>\n" );
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document.write( "95% confidence interval is from 106.6 people to 136.0 people.\r<BR>\n" );
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document.write( "you can see these visually from the following pictures.<BR>\n" );
document.write( "any differences between the numbers shown in the pictures and the numbers i calculated are due to differences in the way the calculators handle the numbers.<BR>\n" );
document.write( "some calculators are consistent with each other, but not all.<BR>\n" );
document.write( "differences are usually due to rounding assumptions and to interpolation assumptions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/090501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/090502.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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