document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189989>Question 1189989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A phone maker claims that its phones’ batteries last for 13.7 hours on average with standard usage with a standard deviation of 0.9 hours.  The distribution of battery lives is normal.\r<BR>\n" );
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document.write( "(a)  If we accept that claim, what is the probability that a battery lasts between 11 and 12 hours?\r<BR>\n" );
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document.write( "(b)  Find the 85th  percentile for the battery lives- that is, a time for which 85% of the <BR>\n" );
document.write( "batteries last less than that time.\r<BR>\n" );
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document.write( "(c)  The company has just tested 19 devices.  Find the probability that the mean battery life of the 19 phones is more than 14 hours.<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 #821514 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=821514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "so z (11 hr)=(11-13.7)/0.9 and z (12 hr)=(12-13.7)/0.9<BR>\n" );
document.write( "on a calculator, use 2ndVARS 2normalcdf(11,12,13.7,0.9) for probability of 0.0281<BR>\n" );
document.write( "Another way has z between -3 and -1.89 for prob. 0.00135 and 0.0294 for the same answer, subtracting the first from the second.<BR>\n" );
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document.write( "85th percentile is z=1.036=(x-13.7)/0.9, and x=14.63 hours.<BR>\n" );
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document.write( "this is z>(x-mean)/sigma/sqrt(n)<BR>\n" );
document.write( "so z>(14-13.7)/0.9/sqrt(19)=1.453<BR>\n" );
document.write( "That has probability of 0.0731<BR>\n" );
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