document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198914>Question 1198914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The reading test scores for the population of fifth graders is normally distributed with a mean of of 55 and a standard deviation of 8. What percentage of fifth graders score more than 47, but less than 71?\r<BR>\n" );
document.write( "\n" );
document.write( "The correct answer is one of the following.  Which one is correct?\r<BR>\n" );
document.write( "\n" );
document.write( "A) 13.5%\r<BR>\n" );
document.write( "\n" );
document.write( "B) 84%\r<BR>\n" );
document.write( "\n" );
document.write( "C) 97.5%\r<BR>\n" );
document.write( "\n" );
document.write( "D) 81.5%\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832586 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=832586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 55<BR>\n" );
document.write( "standard deviation = 8<BR>\n" );
document.write( "want probability of scores between 47 and 71.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability is .8166\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use z-score if you don't have a calculator that does it directly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score formula is z = (x - m) / s<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the low side, formula becomes z = (47 - 55)/8 = -1<BR>\n" );
document.write( "on the high side, formula becomes z = (71 - 55)/8 = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use a calculator or a z-score table to find the area to the left of those z-scores.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area to the left of z-score of -1 = .1586552<BR>\n" );
document.write( "agea to the left of z-score of 2 = .9772499<BR>\n" );
document.write( "area in between = larger area minus smaller area = .81859467<BR>\n" );
document.write( "round to 4 decimal places to get .8186\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability of getting a score between 47 and 71 is equal to .8186.<BR>\n" );
document.write( "that's your answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a calculator i used to get the answer directly is found at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the results from using that calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/120404.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "calculator i used was the ti-84 plus.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you could also use the z-score table, but a calculator is much easier.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );