document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128016>Question 1128016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years.   Let’s suppose that the standard deviation is 1.9 years and that the distribution of lifespans is normal<BR>\n" );
document.write( "Find:  <BR>\n" );
document.write( "(a) the probability that a $5 bill will last more than 4 years.\r<BR>\n" );
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document.write( "(b) the probability that a $5 bill will last between 3 and 5 years.\r<BR>\n" );
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document.write( "(c) the 97th  percentile for the lifespan of these bills (a time such that 97% of bills last less than that time).\r<BR>\n" );
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document.write( "(d ) the probability that a random sample of 37 bills has a mean lifespan of more than 4.5 years.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744479 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=744479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "a.  z=(4-4.9)/1.9=-0.47<BR>\n" );
document.write( "probability z>-0.47 is 0.6808<BR>\n" );
document.write( "b. this is a z between -1.9/1.9 or -1 and .1/1.9 or 0.05<BR>\n" );
document.write( "probability is z between -1 and 0.05, or 0.3613<BR>\n" );
document.write( "c. 97th percentile is z>1.88 <BR>\n" );
document.write( "1.88=(x-4.9)/1.9<BR>\n" );
document.write( "=8.47 years<BR>\n" );
document.write( "d. This is a z> (4.5-4.9)/1.9/sqrt(35), sampling distribution of sample means.<BR>\n" );
document.write( "z> -0.4*sqrt(35)/1.9=-1.25<BR>\n" );
document.write( "probability is 0.8944<BR>\n" );
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