document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203181>Question 1203181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A speed trap on the highway set by the O.P.P. shows that the mean speed of cars is<BR>\n" );
document.write( "103.4 km/h with a standard deviation of 9.8 km/h. The posted speed limit on the<BR>\n" );
document.write( "highway is 100 km/h.<BR>\n" );
document.write( "a. What percentage of drivers are driving under the speed limit? <BR>\n" );
document.write( "b. Speeders caught traveling over 15 km/h over the speed limit are subject to<BR>\n" );
document.write( "losing demerit points. What percentage of speeders will be subject to<BR>\n" );
document.write( "losing demerit points? <BR>\n" );
document.write( "c. What percentage of drivers travel between the speed of 105 km/h and 115<BR>\n" );
document.write( "km/h? <BR>\n" );
document.write( "d. The top 2% of all drivers speeding are subject to losing their license.<BR>\n" );
document.write( "According to the data, what speed must a driver be traveling to lose his or<BR>\n" );
document.write( "her license? <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 #838542 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A speed trap on the highway set by the O.P.P. shows that the mean speed of cars is<BR>\n" );
document.write( "103.4 km/h with a standard deviation of 9.8 km/h. The posted speed limit on the<BR>\n" );
document.write( "highway is 100 km/h.<BR>\n" );
document.write( "a. What percentage of drivers are driving under the speed limit?<BR>\n" );
document.write( "b. Speeders caught traveling over 15 km/h over the speed limit are subject to<BR>\n" );
document.write( "losing demerit points. What percentage of speeders will be subject to<BR>\n" );
document.write( "losing demerit points?<BR>\n" );
document.write( "c. What percentage of drivers travel between the speed of 105 km/h and 115<BR>\n" );
document.write( "km/h?<BR>\n" );
document.write( "d. The top 2% of all drivers speeding are subject to losing their license.<BR>\n" );
document.write( "According to the data, what speed must a driver be traveling to lose his or<BR>\n" );
document.write( "her license?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  This probability is the area under the specified normal curve on the left of\r\n" );
document.write( "     the raw z-score of 100 km/h.\r\n" );
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document.write( "     To determine this probability (= this area), you may use your regular calculator \r\n" );
document.write( "     TI-83 or TI-84, standard function normalcdf. \r\n" );
document.write( "     Alternatively, you may use free of charge online calculator\r\n" );
document.write( "     https://onlinestatbook.com/2/calculators/normal_dist.html \r\n" );
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document.write( "     With TI-83 or TI-84, you have\r\n" );
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document.write( "                         z1     z2  mean   SD     <<<===--- formatting pattern\r\n" );
document.write( "          P = normalcdf(-9999, 100, 103.4, 9.8) = 0.6357.   <U>ANSWER</U>\r\n" );
document.write( "\r\n" );
document.write( "     With online calculator, you have the same answer PLUS a complete visual explanations\r\n" );
document.write( "     on what you do, what the calculator does for you and why it is correct.\r\n" );
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document.write( "(b)  This percentage is the area under the specified normal curve on the right of\r\n" );
document.write( "     the raw z-score 100 + 15 = 115 km/h.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     To determine this probability (= this area), you may use your regular calculator \r\n" );
document.write( "     TI-83 or TI-84, standard function normalcdf. \r\n" );
document.write( "     Alternatively, you may use free of charge online calculator\r\n" );
document.write( "     https://onlinestatbook.com/2/calculators/normal_dist.html \r\n" );
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document.write( "\r\n" );
document.write( "     With TI-83 or TI-84, you have\r\n" );
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document.write( "                         z1     z2  mean   SD     <<<===--- formatting pattern\r\n" );
document.write( "          P = normalcdf( 115, 9999, 103.4, 9.8) = 0.0629.   <U>ANSWER</U>\r\n" );
document.write( "\r\n" );
document.write( "     With online calculator, you have the same answer PLUS a complete visual explanations\r\n" );
document.write( "     on what you do, what the calculator does for you and why it is correct.\r\n" );
document.write( "\r\n" );
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document.write( "(c)                       z1   z2  mean   SD     <<<===--- formatting pattern\r\n" );
document.write( "          P = normalcdf( 105, 115, 103.4, 9.8) = 0.242.   <U>ANSWER</U>\r\n" );
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document.write( "(d)  To answer this question, you need to determine a raw z-score such that the area \r\n" );
document.write( "     under the normal curve is 2% on the right of it, or 98% on the left of it.\r\n" );
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document.write( "\r\n" );
document.write( "     To determine this z-score, you may use your regular calculator \r\n" );
document.write( "     TI-83 or TI-84, standard function invNorm. \r\n" );
document.write( "     Alternatively, you may use free of charge online calculator\r\n" );
document.write( "     https://onlinestatbook.com/2/calculators/inverse_normal_dist.html\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     With TI-83 or TI-84, you have\r\n" );
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document.write( "                       area  mean   SD     <<<===--- formatting pattern\r\n" );
document.write( "          P = invNorm( 0.98, 103.4, 9.8) = 123.527.   <U>ANSWER</U>\r\n" );
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document.write( "     It is the maximum allowed speed. All drivers overspeeding are to lose his or her license.\r\n" );
document.write( "\r\n" );
document.write( "     With online calculator, you have the same answer PLUS a complete visual explanations\r\n" );
document.write( "     on what you do, what the calculator does for you and why it is correct.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved, with complete explanations.\r<BR>\n" );
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document.write( "To learn more on standard functions normalcdf and invNorm, look into these Internet web-sources\r<BR>\n" );
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document.write( "https://www.tcc.fl.edu/media/divisions/learning-commons/resources-by-subject/math/statistics/Choosing-whether-to-use-normalcdf-or-invNorm.pdf\r<BR>\n" );
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document.write( "https://courses.lumenlearning.com/introstats1/chapter/using-the-normal-distribution/\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );