document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747311>Question 747311</A>: <I><SPAN STYLE=\"word-break: break-all;\">  On the daily run of an express bus, the average number of passengers is 48. The<BR>\n" );
document.write( " standard deviation is 3.  Assume the variable is normally distributed. Find the probability that the bus will have fewer than 42?\r<BR>\n" );
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document.write( "more than 48?<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 #454830 by </B><A HREF=/tutors/aboutme.mpl?userid=mikeebsc><B>mikeebsc(26)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mikeebsc><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this we have to understand that average and \"mean\" are the same thing so:\r<BR>\n" );
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document.write( "LESS THAN 42:<BR>\n" );
document.write( "We must first find he z-score using the formula: x-mean/Std.Dev. **or**\r<BR>\n" );
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document.write( "(42-48)/3=-2\r<BR>\n" );
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document.write( "Now we find the corresponding z score to -2.0 using the standard normal distribution table which = .0228 so:\r<BR>\n" );
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document.write( "P(x<42)=.0228\r<BR>\n" );
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document.write( "If you are allowed to use a calculator: using a TI-83 or TI-84 the steps are:\r<BR>\n" );
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document.write( "2nd DISTR\r<BR>\n" );
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document.write( "scroll down to normalcdf\r<BR>\n" );
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document.write( "lowerbound=-1,000,000 *this represents a number large enough to approximate - infinity as we are looking for EVERYTHING under 42 (make sure to use a neg sign and not the minus sign)\r<BR>\n" );
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document.write( "upperbound=42\r<BR>\n" );
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document.write( "mean=48\r<BR>\n" );
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document.write( "Std. Dev.=3\r<BR>\n" );
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document.write( "Press enter twice and you get .02275, or .0228; the same as if you had used the standard normal distribution table.\r<BR>\n" );
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document.write( "MORE THAN 48:<BR>\n" );
document.write( "Again we find the z-score using the formula x-mean/Std.Dev. **or**\r<BR>\n" );
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document.write( "(48-48)/3 = 0\r<BR>\n" );
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document.write( "Now we find the corresponding z score to 0 using the standard normal distribution table which = .5000 so:\r<BR>\n" );
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document.write( "P(x>48)=.5000\r<BR>\n" );
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document.write( "You can use the same calculator steps replacing upperbound with 48 to find your answer or check your work.\r<BR>\n" );
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document.write( "Hope this helps!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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