document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192124>Question 1192124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain company manufactures precision thermometers that are supposed to give readings of 0.00° C at the freezing point of water. Tests on a large sample of these thermometers reveal that some give readings above 0.00° C and some give readings below 0.00° C. Suppose thermometer readings are approximately normally distributed with mean thermometer 0.00° C with a standard deviation of 1.00°. What is the thermometer reading that separates the top 4% of readings from the rest? (Round your answer to two decimal places; add trailing zeros as needed.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824039 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=824039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Use a calculator like this<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://davidmlane.com/normal.html\">https://davidmlane.com/normal.html</a><BR>\n" );
document.write( "Click \"Value from an area\"<BR>\n" );
document.write( "Input 0.04 as the area<BR>\n" );
document.write( "Input 0 as the mean<BR>\n" );
document.write( "Input 1 as the standard deviation<BR>\n" );
document.write( "Click the \"above\" option and hit \"recalculate\" to have 1.751 result.<BR>\n" );
document.write( "This means that 4% of the area is to the right of 1.751\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This rounds to 1.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Alternative Path\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you want to use a table instead of a calculator, then you can use something like this<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net\">https://www.ztable.net</a><BR>\n" );
document.write( "Locate 0.04 in the table or try to get as close as you can to it.<BR>\n" );
document.write( "The value 0.04006 is as close as we can get<BR>\n" );
document.write( "Trace to the left until you get to -1.7 at the very left<BR>\n" );
document.write( "Trace up the column until you arrive at 0.05 at the very top<BR>\n" );
document.write( "Refer to the diagram below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"65%\" src = \"https://i.imgur.com/TQtsZFf.png\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The headers -1.7 and 0.05 combine to -(1.7+0.05) = -1.75<BR>\n" );
document.write( "This shows P(Z < -1.75) = 0.04006 approximately<BR>\n" );
document.write( "Due to mirror symmetry, we can say P(Z > 1.75) = 0.04006 approximately\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, we can see that 1.75 is the top 4% cut off point, aka its the value of the 96th percentile since about 96% of the distribution is below z = 1.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: 1.75<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );