document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058647>Question 1058647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 3.5 hours and a standard deviation of 3 hours. Show all work. Just the answer, without supporting work, will receive no credit.<BR>\n" );
document.write( "(a) Find the 80th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places)<BR>\n" );
document.write( "(b) What is the probability that a randomly selected adult has more than 7 hours of exercise per week? (round the answer to 4 decimal places) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673735 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=673735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 80th percentile is p=0.8000 on the std normal curve<BR>\n" );
document.write( "z=0.842<BR>\n" );
document.write( "z=(x-mean)/sd<BR>\n" );
document.write( "0.842=(x-3.5)/3<BR>\n" );
document.write( "2.526=x-3.5<BR>\n" );
document.write( "x=6.026 or 6.03 hours. That is 2.53 above the mean or 0.84 sd or 80th percentile.<BR>\n" );
document.write( "more than 7 hours<BR>\n" );
document.write( "z=(7-3.5)/3=3.5/3=1.167<BR>\n" );
document.write( "for z>1.167, the probability is 0.1216 or 0.12.<BR>\n" );
document.write( "It is more than 1 sd, above which is about 15% of the probability, so this makes sense. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );