document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181573>Question 1181573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The heights of 200 plants in a garden follow a normal distribution with a mean of 72.3 cm with a standard<BR>\n" );
document.write( "deviation of 8.9 cm.<BR>\n" );
document.write( "a. about how many plants whose heights are between 82 and 90 cm?<BR>\n" );
document.write( "b. about how many plants whose heights are between 70 and 75 cm?<BR>\n" );
document.write( "c. if 20% of the tallest plants are to be trimmed, then what is the starting height of the plants that the<BR>\n" );
document.write( "gardener must choose to trim? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811819 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=811819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "a. z=9.7/8.9 and 17.7/8.9 or 1.09 and 1.99.  That probability is 0.1146<BR>\n" );
document.write( "b. z=-2.3/8.9 and 2.7/8.9 or -0.26 and 0.30 with probability of 0.2204<BR>\n" );
document.write( "check with 2nd VARS2normalcddf(82,90,72.3,8.9) which is more accurate because the z-values above were rounded, But it is only to the fourth decimal place in the first and 0.0008 different in the second. Ask how accurate it should be.<BR>\n" );
document.write( "c.80th percentile has a z of 0.8416. (can use 3invnorm(0.80,0,1) to get the z-value<BR>\n" );
document.write( "so 0.846=(x-72.3)/8.9<BR>\n" );
document.write( "7.49=x-72.3<BR>\n" );
document.write( "x=79.8 cm </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );