document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192123>Question 1192123</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 46 batteries and determine whether each is within specifications. The entire shipment will be accepted if at most 2 of the batteries do not meet specifications. Suppose a certain shipment contains 7,000 batteries, and 2% of them do not meet specifications. What is the probability that this entire shipment of 7,000 batteries will be accepted? (Round your answer to three decimal places; add trailing zeros 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 #849084 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem using the binomial probability formula:\r<BR>\n" );
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document.write( "**1. Define the variables:**\r<BR>\n" );
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document.write( "* n = 46 (sample size)<BR>\n" );
document.write( "* p = 0.02 (probability of a battery not meeting specifications)<BR>\n" );
document.write( "* k = number of batteries not meeting specifications (0, 1, or 2 for acceptance)\r<BR>\n" );
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document.write( "**2. Calculate the probabilities:**\r<BR>\n" );
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document.write( "We need to calculate the probability of 0, 1, or 2 batteries not meeting specifications and then add these probabilities together. The binomial probability formula is:\r<BR>\n" );
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document.write( "P(x) = (nCx) * p^x * (1-p)^(n-x)\r<BR>\n" );
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document.write( "Where nCx is the number of combinations of n items taken x at a time (also written as \"n choose x\").\r<BR>\n" );
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document.write( "* P(0) = (46C0) * (0.02)^0 * (0.98)^46 ≈ 0.396<BR>\n" );
document.write( "* P(1) = (46C1) * (0.02)^1 * (0.98)^45 ≈ 0.372<BR>\n" );
document.write( "* P(2) = (46C2) * (0.02)^2 * (0.98)^44 ≈ 0.168\r<BR>\n" );
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document.write( "**3. Add the probabilities:**\r<BR>\n" );
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document.write( "P(acceptance) = P(0) + P(1) + P(2) ≈ 0.396 + 0.372 + 0.168 ≈ 0.936\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "The probability that the entire shipment will be accepted is approximately 0.936.<BR>\n" );
document.write( " </SPAN>\n" );
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