document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768269>Question 768269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer of automobile batteries claims that the distribution of the lengths of life of its best battery has a mean of 54 months and a standard deviation of 6 months.  Recently, the manufacturer has received a number of complaints from unsatisfied customers whose batteries died earlier than expected.  A consumer group decides to check the manufacturer's claim by purchasing a SAMPLE of 50 batteries and subjecting them to tests to determine battery life.  \r<BR>\n" );
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document.write( "Assuming that the manufacturer's claim is true that the mean is 54 and the standard deviation is 6, what is the probability the consumer group's sample will have a mean life of 52 or fewer months? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468191 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A manufacturer of automobile batteries claims that the distribution of the lengths of life of its best battery has a mean of 54 months and a standard deviation of 6 months. Recently, the manufacturer has received a number of complaints from unsatisfied customers whose batteries died earlier than expected. A consumer group decides to check the manufacturer's claim by purchasing a SAMPLE of 50 batteries and subjecting them to tests to determine battery life. <BR>\n" );
document.write( "Assuming that the manufacturer's claim is true that the mean is 54 and the standard deviation is 6, what is the probability the consumer group's sample will have a mean life of 52 or fewer months?<BR>\n" );
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document.write( "mean of the sample means::: 54 mths<BR>\n" );
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document.write( "std of sample means::: 6/sqrt(50) = 0.8485<BR>\n" );
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document.write( "z(52) = (52-54)/0.8485 = -2.3570<BR>\n" );
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document.write( "P(x-bar < 52) = P(z < -2.3570) = 0.0092<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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