document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204105>Question 1204105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 38 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 7000 ​batteries, and ​2% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected? The probability that this whole shipment will be accepted is    enter your response here.​(Round to four decimal places as​ needed.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840138 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability thqt the whole shipment will be accepted is equal to 0.993131178 this is approximately 99.31% when the percent is rounded to 2 decimal places.<BR>\n" );
document.write( "that's the probability that less than or equal to 3 batteries in a sample of 38 batteries will be defective.<BR>\n" );
document.write( "the probability that more than 3 batteries will be rejected in a random sample of 38 is equal to 100% - 99.31% = .69%.\r<BR>\n" );
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document.write( "i considered this a binomial probability problmm.<BR>\n" );
document.write( "the calculations were done in excel.\r<BR>\n" );
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document.write( "the formula for each probability is p(x) = p^x * q^(n-x) * c(n,x)<BR>\n" );
document.write( "for example, the probability that 3 will be rejected is:<BR>\n" );
document.write( "p(3) = .02^3 * .98^(38-3) * c(38,3) = 0.03327662.<BR>\n" );
document.write( "that's the same number for p(3) in the spreadsheet.<BR>\n" );
document.write( "c(n,x) = n! / (x! * (n-x)!).<BR>\n" );
document.write( "that becomes c(38,3) = 38! / (3! * (38-3)!) which is equal to 8436.<BR>\n" );
document.write( "this is the same number in the spreadsheet for p(3).\r<BR>\n" );
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document.write( "here's the spreadsheet with all the calculations.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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