document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200150>Question 1200150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 15 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.\r<BR>\n" );
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document.write( "a. What is the distribution of X? X ~ N(<BR>\n" );
document.write( "(15,6)<BR>\n" );
document.write( "Correct \r<BR>\n" );
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document.write( "b. If one of the trials is randomly chosen, find the probability that it lasted at least 17 days. <BR>\n" );
document.write( "Correct: 0.3694\r<BR>\n" );
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document.write( "c. If one of the trials is randomly chosen, find the probability that it lasted between 14 and 18 days. <BR>\n" );
document.write( "0.2576<BR>\n" );
document.write( "Correct \r<BR>\n" );
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document.write( "d. 80% of all of these types of trials are completed within how many days? (Please enter a whole number) \r<BR>\n" );
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document.write( "* I need help with letter B on finding at least in normal distribution and letter D on a TI-84 Calculator <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 #834188 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (b)\r<BR>\n" );
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document.write( "On your TI84 calculator, press the button labeled \"2nd\" in the upper left corner.<BR>\n" );
document.write( "Then press the VARS key to bring up the stats distribution menu.\r<BR>\n" );
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document.write( "The function we're after is <font color=blue>normalcdf</font> which finds the area under the normal distribution curve.\r<BR>\n" );
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document.write( "The template is <font color=blue>normalcdf(L, U, mu, sigma)</font><BR>\n" );
document.write( "L = lower boundary<BR>\n" );
document.write( "U = upper boundary<BR>\n" );
document.write( "mu = mean<BR>\n" );
document.write( "sigma = standard deviation\r<BR>\n" );
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document.write( "In the case of part (b), we have<BR>\n" );
document.write( "L = 17<BR>\n" );
document.write( "U = 9999, or any other very large value to represent positive infinity<BR>\n" );
document.write( "mu = 15<BR>\n" );
document.write( "sigma = 6\r<BR>\n" );
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document.write( "This means you would type in <font color=blue>normalcdf(17,9999,15,6)</font>\r<BR>\n" );
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document.write( "Your calculator should produce the approximate result of 0.3694414037 which rounds to 0.3694 when rounding to four decimal places.\r<BR>\n" );
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document.write( "Answer to part (b): <font color=red size=4>0.3694</font>\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "We're looking for a value of k such that<BR>\n" );
document.write( "P(X < k) = 0.80<BR>\n" );
document.write( "we want to know the cut-off point between the lower 80% and the upper 20%\r<BR>\n" );
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document.write( "The function we want is called <font color=blue>invNorm</font> <BR>\n" );
document.write( "This can be found in the same menu as normalcdf. It's in the 3rd slot.\r<BR>\n" );
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document.write( "The template for this function is<BR>\n" );
document.write( "<font color=blue>invNorm(p, mu, sigma)</font><BR>\n" );
document.write( "where,<BR>\n" );
document.write( "p = area under the normal curve between 0 and 1<BR>\n" );
document.write( "mu = mean<BR>\n" );
document.write( "sigma = standard deviation\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "p = 0.80<BR>\n" );
document.write( "mu = 15<BR>\n" );
document.write( "sigma = 6\r<BR>\n" );
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document.write( "So you should type in <font color=blue>invNorm(0.80, 15, 6)</font><BR>\n" );
document.write( "The calculator will produce a result of roughly 20.0497274<BR>\n" );
document.write( "That rounds to 20 when rounding to the nearest whole number.\r<BR>\n" );
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document.write( "So we can say that<BR>\n" );
document.write( "P(X < 20) = 0.80<BR>\n" );
document.write( "approximately.\r<BR>\n" );
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document.write( "About 80% of the trials finish within 20 days (i.e. 20 days or fewer).\r<BR>\n" );
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document.write( "Answer to part (d) is <font color=red size=4>20</font><BR>\n" );
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