document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196439>Question 1196439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The salary of assistant professors at Kent State University is normally distributed with a mean of $45,000 and a standard deviation of $1,500.If I chose an assistant professor at random, what is the probability that he/she makes more than 1.3 standard deviations above the mean?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829281 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.3 standard deviations above the mean gives you a z-score of 1.3<BR>\n" );
document.write( "area to the right of a z-score of 1.3 = .0968005494.<BR>\n" );
document.write( "i used the ti-84 plus to get that number.<BR>\n" );
document.write( "the z-score table would give you 1 - .90320 = .09680.<BR>\n" );
document.write( "if you round to 4 decimal places, the answer will be the same as .0968.<BR>\n" );
document.write( "i confirmed using david lane calculator.<BR>\n" );
document.write( "1.3 * 1500 = 1950<BR>\n" );
document.write( "add that to 45000 to get 46950<BR>\n" );
document.write( "results from david lane calculator are shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/091701.jpg\" ><BR>\n" );
document.write( "results from z-score table are shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/091702.jpg\" ><BR>\n" );
document.write( "david lane calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "z-score table at <a  rel=nofollow HREF= \"https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf\" target = \"_blank\">https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf</a><BR>\n" );
document.write( "note that the z-score table gives you area to the left of the z-score.<BR>\n" );
document.write( "area to the right is 1 minus that.<BR>\n" );
document.write( "note that if you used the z-score formula to get the z-score, you would have gotten z-score of 1.3 as shown below.<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw mean<BR>\n" );
document.write( "s is the standard deviation.<BR>\n" );
document.write( "formula becomes z = (46950 - 45000) / 1500 = = 1950 / 1500 = 1.3.<BR>\n" );
document.write( "46950 is 45000 + 1.3 * 1500 which is 1.3 standard deviations above the mean. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );