document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=364862>Question 364862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A phone company has determined that the length of its customers' calls is normally with a mean of 2.87 minutes and a standard deviation of 1.51 minutes. \r<BR>\n" );
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document.write( "Find the probability that a customers' call will last for more than 4 minutes. \r<BR>\n" );
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document.write( "the probability that a customer's call will last between 1.1 and 3.2 minutes. \r<BR>\n" );
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document.write( "the 21st percentile for the length of telephone calls (a time such that 21% of calls are less than that time)\r<BR>\n" );
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document.write( "the probability that a random sample of 30 calls has a mean length of more than 3.43minutes  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260120 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=260120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A phone company has determined that the length of its customers' calls is normally with a mean of 2.87 minutes and a standard deviation of 1.51 minutes.<BR>\n" );
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document.write( "Find the probability that a customers' call will last for more than 4 minutes.<BR>\n" );
document.write( "z(4) = (4-2.87)/1.51 = 0.7483<BR>\n" );
document.write( "P(x > 4) = P(z > 0.7483) = 0.2271<BR>\n" );
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document.write( "the probability that a customer's call will last between 1.1 and 3.2 minutes.<BR>\n" );
document.write( "Find the z-values of 1.1 and 3.2<BR>\n" );
document.write( "Find the area under the normal curve over that z interval.<BR>\n" );
document.write( "I get: 0.4659<BR>\n" );
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document.write( "the 21st percentile for the length of telephone calls (a time such that 21% of calls are less than that time)<BR>\n" );
document.write( "invNorm(0.21) = -0.8064<BR>\n" );
document.write( "x = -0.8064*1.51+2.87 = 1.6523<BR>\n" );
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document.write( "the probability that a random sample of 30 calls has a mean length of more than 3.43minutes<BR>\n" );
document.write( "t(3.43) = (3.43-2.87)/[1.51/sqrt(30)] = 2.0313<BR>\n" );
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document.write( "P(x-bar < 3.43) = P(t> 2.0313 when df=29) = 0.0257<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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