document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130977>Question 130977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this question.\r<BR>\n" );
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document.write( "Question: The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100 degree C) is normally distributed with mean &#956; = 99.8 degree C and standard deviation &#963; = 0.1 degree C. [Please draw a density curve before you do any calculations.]\r<BR>\n" );
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document.write( "1). What is the probability that the thermometer reading is greater than 100 degree C?\r<BR>\n" );
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document.write( "2). What is the probability that the thermometer reading is exactly 100 degree C?\r<BR>\n" );
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document.write( "3). What is the probability that the thermometer reading is within ± 0.05 degree C?<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 #95747 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=95747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100 degree C) is normally distributed with mean &#956; = 99.8 degree C and standard deviation &#963; = 0.1 degree C. [Please draw a density curve before you do any calculations.] <BR>\n" );
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document.write( "Draw a normal curve; put mean = 99.8.<BR>\n" );
document.write( "Calculate the z-value of the termperature in each of the problems using<BR>\n" );
document.write( "z(x) = (x-mu)/sigma<BR>\n" );
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document.write( "1). What is the probability that the thermometer reading is greater than 100 degree C?<BR>\n" );
document.write( "z(100) = (100-99.8)/0.1 = 0.02/0.1 = 0.2<BR>\n" );
document.write( "P(z>0.2) = 0.4207<BR>\n" );
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document.write( "2). What is the probability that the thermometer reading is exactly 100 degree C? <BR>\n" );
document.write( "The probability of any particular value is zero<BR>\n" );
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document.write( "3). What is the probability that the thermometer reading is within ± 0.05 degree C?<BR>\n" );
document.write( "I'll assume you mean within 0.05 degrees of the mean.<BR>\n" );
document.write( "Find the z-value of 99.8+0.05= 99.85<BR>\n" );
document.write( "z(99.85) = (99.85-99.8)/0.1 = 0.5<BR>\n" );
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document.write( "P(99.8-0.05 < temp < 99.5+0.05) = P(-0.5 < z < 0.5) = 0.3829<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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