document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970787>Question 970787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 3-4, for a normal standard distribution, determine what percent of the data values are in each given range.<BR>\n" );
document.write( "3. Between 1 standard deviation below the mean and 1 standard deviation above the mean<BR>\n" );
document.write( "4. Berween 1 standard deviation below the mean and 2 standard deviation above the mean\r<BR>\n" );
document.write( "\n" );
document.write( "This question has been bothering me so much, I need help thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593449 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a normal distribution, z-score is on the left of the table, and the four figures in the table are probabilities.\r<BR>\n" );
document.write( "\n" );
document.write( "1 SD below =0.1586 probability from the left end to z=-1  (50% probability from left end to z=0)<BR>\n" );
document.write( "1 SD above=0.1586 from right.\r<BR>\n" );
document.write( "\n" );
document.write( "That sum is 0.3172\r<BR>\n" );
document.write( "\n" );
document.write( "Subtract from 1, and what is left is between -1 and 1  is  0.6828<BR>\n" );
document.write( "68% of the probability is between -1 and +1 SD\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From -1 to +2<BR>\n" );
document.write( "0.1584  to the left is excluded as before.<BR>\n" );
document.write( "Go to the z-table, and under 2.0 you see 0.4772, depending on the z-table (might be 0.9772)  The 0.4772 is z above 50%; the 0.9772 is the total probability from the left side to z=+2<BR>\n" );
document.write( "+2 has 0.4772 probability (from 50%). \r<BR>\n" );
document.write( "\n" );
document.write( "Another way to do it is to take the 0.9772 (z=2; 2 SDs) and subtract 0.1586, which is to the LEFT of z=-1 (that is not what you want).  In between is what you want, and the probability is the difference of the two numbers, 0.8186.   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );