document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012445>Question 1012445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 15. Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph. \r<BR>\n" );
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document.write( "a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?\r<BR>\n" );
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document.write( "b. What proportion of the vehicles would be going less than 50 mph?\r<BR>\n" );
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document.write( "c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628380 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=628380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph. <BR>\n" );
document.write( "a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?<BR>\n" );
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document.write( "z(65) = (65-71)/8 = -6/8 = = -3/4<BR>\n" );
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document.write( "P(x <= 65) = P(z <= -3/4) = normalcdf(-100,-3/4) = 0.2266<BR>\n" );
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document.write( "b. What proportion of the vehicles would be going less than 50 mph?<BR>\n" );
document.write( "z(50) = (50-71)/8 = -2.625<BR>\n" );
document.write( "P(x < 50) = P(z < -2.625) = normalcdf(-100,-2.625) = 0.0043<BR>\n" );
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document.write( "c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?<BR>\n" );
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document.write( "Find the z-value with a left tail of 90%::<BR>\n" );
document.write( "invNorm(0.90) = 1.2816<BR>\n" );
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document.write( "Find the corresponding speed limit::<BR>\n" );
document.write( "x = 1.2816*8 + 71 = 81.25<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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