document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638305>Question 638305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . A radar unit is used to measure the speed of automobile on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a standard deviation of 4 mph.\r<BR>\n" );
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document.write( "a. Find the mean of all speeds if 3% of the automobiles travel faster than 72 mph. Round the mean to the nearest tenth.\r<BR>\n" );
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document.write( "b. Using the mean you found in part a, find the probability that a car is traveling between 70 mph and 75 mph. Interpret the meaning of this answer.\r<BR>\n" );
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document.write( "c. Using the mean you found in part a, find the 25th percentile for the variable \"speed\".<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 #402123 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=402123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A radar unit is used to measure the speed of automobile on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a standard deviation of 4 mph.<BR>\n" );
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document.write( "Sketch a normal curve with u = ? and sigma = 4<BR>\n" );
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document.write( "a. Find the mean of all speeds if 3% of the automobiles travel faster than 72 mph. Round the mean to the nearest tenth.<BR>\n" );
document.write( "Mark a point on the horizontal axis with a right-tail of 3%.<BR>\n" );
document.write( "Mark the point as x = 72.<BR>\n" );
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document.write( "Find the z-value that has a right tail of 3%:<BR>\n" );
document.write( "invNorm(0.97) = 1.8808<BR>\n" );
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document.write( "Now find \"u\":<BR>\n" );
document.write( "x = z*s + u<BR>\n" );
document.write( "72 = 1.8808*4 + u<BR>\n" );
document.write( "u = 64.4768 = 64.5 mph when rounded<BR>\n" );
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document.write( "b. Using the mean you found in part a, find the probability that a car is traveling between 70 mph and 75 mph. Interpret the meaning of this answer.<BR>\n" );
document.write( "z(70) = (70-64.5)/4 = 1.375<BR>\n" );
document.write( "z(75) = (75-64.5)/4 = 2.625<BR>\n" );
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document.write( "P(70<= x <=75) = P(1.375<= z <=2.625) = 0.08<BR>\n" );
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document.write( "c. Using the mean you found in part a, find the 25th percentile for the variable \"speed\".<BR>\n" );
document.write( "Find the z-value with a left-tail of 25%<BR>\n" );
document.write( "invNorm(0.25) = -0.6745<BR>\n" );
document.write( "Find the corresponding x value:<BR>\n" );
document.write( "x = zs+u = -0.6745*4+64.5 = 61.8 mph<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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