document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192350>Question 1192350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.22 grams per mile (g/mi) and standard deviation 0.059 g/mi. Government regulations call for NOX emissions no higher than 0.28 g/mi.\r<BR>\n" );
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document.write( "A) What is the probability (±0.001) that a single-car of this model fails to meet the NOX requirement? \r<BR>\n" );
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document.write( "B) A company has 15 cars of this model in its fleet. What is the probability (±0.001) that the average NOX level x of these cars is above the 0.28 g/mi limit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824380 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=824380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = .22 grams per mile.<BR>\n" );
document.write( "standard deviation = .059 grams per mile.<BR>\n" );
document.write( "test level of NOX = 28 grams per mile.\r<BR>\n" );
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document.write( "z-score formula is z = (x - m) / s.<BR>\n" );
document.write( "s represents the standard deviation when applied to a sample of one single element.<BR>\n" );
document.write( "z-score formula is z = (x - m) / s.<BR>\n" );
document.write( "s represents the standard error when applied to the mean of a sample of n elements.<BR>\n" );
document.write( "the formula for standard error is that s = standard deviation divided by square root of sample size.\r<BR>\n" );
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document.write( "the first part of your problem is looking at a sample of one single element.<BR>\n" );
document.write( "the z-score formula becomes:<BR>\n" );
document.write( "z = (x - m) / s becomes z = (.28 - .22) / .059.<BR>\n" );
document.write( "solve for z to get z = 1.016949153.<BR>\n" );
document.write( "it's best to use a calculator to find the area to the right of that z-score.<BR>\n" );
document.write( "using my ti-84 plus, i get the area to the right of that z-score = .1545888216.<BR>\n" );
document.write( "that's the probability of getting a sample of one element having having NOX emissions greater than .28 grams per mile.<BR>\n" );
document.write( "round that to 3 decimal places and it will be equal to .155.\r<BR>\n" );
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document.write( "the second part of your problem is looking at a sample of 15 elements.<BR>\n" );
document.write( "here, you would use the standard error, rather than the standard deviation.<BR>\n" );
document.write( "the standard error formula is s = standard deviation divided by the square root of the sample size.<BR>\n" );
document.write( "that becomes s = .059 / sqrt(15) = .0152337345.<BR>\n" );
document.write( "the z-score formula becomes z = (.28 - .22) / .0152337345 = 3.938627132.<BR>\n" );
document.write( "using my ti-84 plus, i get the area to the right of that z-score = .0004099196854.<BR>\n" );
document.write( "that's the probability of getting a sample of 15 elements having a mean of NOX emissions greater than .28 grams per mile.<BR>\n" );
document.write( "round that to 3 decimal places and it will be equal to 0.\r<BR>\n" );
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document.write( "the mean of the sample will get closer to the mean of the population as the sample size gets larger.<BR>\n" );
document.write( "that's a basic principle being applied through the use of the standard error formula.<BR>\n" );
document.write( "since the mean of the population was .22, then it became extremely unlikely that the mean of the sample of 15 elements would be greater than .28.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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