document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194872>Question 1194872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.5% or more are defective, they call repair technicians for service.<BR>\n" );
document.write( "The control department is going to take a random sample of 4400 light bulbs. Let  be the proportion of defective light bulbs in the sample assuming the machinery is working correctly.\r<BR>\n" );
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document.write( "(a)Find the mean of p̂.\r<BR>\n" );
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document.write( "(b)Find the standard deviation of p̂.\r<BR>\n" );
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document.write( "(c)Compute an approximation for P(p̂ >0.015), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.\r<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 #827161 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=827161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4400*0.01=44=np units number of bulbs<BR>\n" );
document.write( "the variance is np(1-p)=44*0.99=43.56 units # of bulbs^2<BR>\n" );
document.write( "the sd is sqrt(43.56)=6.6 units number of bulbs<BR>\n" );
document.write( "for 0.015% or 66 bulbs, an approximation would be z>(66.5-44)/6.6=3.41. I use 66.5 because of the continuity correction factor, and the number has to be greater than 66.<BR>\n" );
document.write( "probability z>3.41 is 0.0003 </SPAN>\n" );
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