document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195499>Question 1195499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> more normal distribution that i need help understanding. and learning how to use technology to help. thank you.\r<BR>\n" );
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document.write( "Suppose that Denver workers have a mean commute of 22 minutes and commute times are normally distributed with a standard deviation of 15 minutes. Let X represent the commute time for a randomly selected Denver worker.\r<BR>\n" );
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document.write( "Find the 85th percentile for the commute time of Denver workers. Round your answer to 1 decimal place.\r<BR>\n" );
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document.write( "The 85th percentile is      minutes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828017 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=828017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 22 minutes.<BR>\n" );
document.write( "the standard deviation is 15 minutes.<BR>\n" );
document.write( "85th percentile means that 85% have a commute time less than 22 minutes.<BR>\n" );
document.write( "this means that 15% have a commute time greater than 22 minutes.<BR>\n" );
document.write( "z-score is equal to (x - m) / s<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation, in this case.<BR>\n" );
document.write( "you are looking for a z-score that has 85% of all z-scores less than that.<BR>\n" );
document.write( "using a statistical calculator, you find that the z-score that has 85% of the commute time less than it would be equal to 1.03643338.<BR>\n" );
document.write( "use the z-score formula to find the raw score.<BR>\n" );
document.write( "z = (x - m) / s becomes 1.03643338 = (x - 22) / 15.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 15 * 1.03643338 + 22 = 37.5465007 minutes.<BR>\n" );
document.write( "that's the commute time that is in the 85th percentile, meaning that 85% of all commute times with a mean of 22 minutes and a standard deviation of 15 minutes will have a commute time less than that.<BR>\n" );
document.write( "you can use a z-score calculator online to confirm that.<BR>\n" );
document.write( "the online calculator that i used is at <a  rel=nofollow HREF= \"https://www.calculator.net/z-score-calculator.html\" target = \"_blank\">https://www.calculator.net/z-score-calculator.html</a><BR>\n" );
document.write( "the results from using that calculator are shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/071503.jpg\"><BR>\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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