document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197941>Question 1197941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.\r<BR>\n" );
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document.write( "It is estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 781 high school seniors, find the following probabilities. (Round your answers to four decimal places.)<BR>\n" );
document.write( "(a) 15 or more will live beyond their 90th birthday\r<BR>\n" );
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document.write( "(b) 30 or more will live beyond their 90th birthday\r<BR>\n" );
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document.write( "(c) between 25 and 35 will live beyond their 90th birthday\r<BR>\n" );
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document.write( "(d) more than 40 will live beyond their 90th birthday<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 #831414 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Binomial Distribution:<BR>\n" );
document.write( "n = 781 ,  p = .035<BR>\n" );
document.write( " 781*.035  and 781*.965  are > 5<BR>\n" );
document.write( "Using the normal approximation and continuity correction factor.<BR>\n" );
document.write( "(the continuity correction factor used as a Binomial Distribution is not continuous)<BR>\n" );
document.write( " mean =781*.035= 27.335<BR>\n" );
document.write( "   sd = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28781%2A.035%2A.965%29 ALIGN=MIDDLE  ALT=\"sqrt%28781%2A.035%2A.965%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5.136<BR>\n" );
document.write( "Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus<BR>\n" );
document.write( "P(x  ≥  15 ) = normpdf(-9999 14.5,  27.335,5.136)= .0062<BR>\n" );
document.write( "P(x  ≥  30 ) = normpdf(-9999 29.5,  27.335,5.136)= .6633<BR>\n" );
document.write( "P( 25 ≤ x ≤ 35) = normcdf( 24.5,35.5,  27.335,5.136) = .6536<BR>\n" );
document.write( "P(x > 40) = normpdf(40.5,9999, 27.335,5.136) = .0052 </SPAN>\n" );
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