document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142730>Question 1142730</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 known that 83% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 62 new products, find the following probabilities. (Round your answers to four decimal places.)<BR>\n" );
document.write( "(a) within 2 years 47 or more fail <BR>\n" );
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document.write( "(b) within 2 years 58 or fewer fail <BR>\n" );
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document.write( "(c) within 2 years 15 or more succeed <BR>\n" );
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document.write( "(d) within 2 years fewer than 10 succeed <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 #763800 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=763800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is np=62*0.83=51.46<BR>\n" );
document.write( "variance is np(1-p)=51.46*0.17=8.7482<BR>\n" );
document.write( "sd is sqrt (V)=2.96<BR>\n" );
document.write( "47 or more use 46.5 as continuity correction factor<BR>\n" );
document.write( "z>(46.5-51.46)/2.96=-1.68<BR>\n" );
document.write( "0.9535\r<BR>\n" );
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document.write( "58 or fewer use 58.5<BR>\n" );
document.write( "(58.5-51.46)/2.96 or z<2.38 with probability of 0.9913\r<BR>\n" );
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document.write( "15 or more succeed is 47 or fewer fail<BR>\n" );
document.write( "z< (47-51.46)/2.96=-1.51<BR>\n" );
document.write( "that has probability of 0.0655\r<BR>\n" );
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document.write( "fewer than 10 succeed means no more than 9 do which means that at least 53 fail.<BR>\n" );
document.write( "z>(53-51.46)/2.96 or z>0.52 0.3015 probability.\r<BR>\n" );
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