document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836010>Question 836010</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 4mph.\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. \r<BR>\n" );
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document.write( "b. using the mean you found in a, find the probability that a car is traveling between 70mph and 75mph. (considering normal probability distribution)\r<BR>\n" );
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document.write( "c. using the mean in a, find the 25th percentile for the variable \"speed\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504017 by </B><A HREF=/tutors/aboutme.mpl?userid=new_user><B>new_user(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=new_user><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=504017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Let the mean be represented by M.\r<BR>\n" );
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document.write( "Critical Z value: Z* = (X - M)/S\r<BR>\n" );
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document.write( "S = Population standard deviation = 4 mph<BR>\n" );
document.write( "X = Test statistic = 72 mph\r<BR>\n" );
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document.write( "Given p(X>72) = 0.03 i.e. p(X<=72) = 1 - 0.03 = 0.97\r<BR>\n" );
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document.write( "Using standard normal distribution table<BR>\n" );
document.write( "So for p = 0.97, Z* = 1.88\r<BR>\n" );
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document.write( "1.88 = (72 - M)/4<BR>\n" );
document.write( "M = 64.48\r<BR>\n" );
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document.write( "So mean speed is 64.48 mph.\r<BR>\n" );
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document.write( "If you need help with the rest then contact me.\r<BR>\n" );
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document.write( "Cheers! </SPAN>\n" );
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