document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181469>Question 1181469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5 days and standard deviation of 1.5 days. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.\r<BR>\n" );
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document.write( "a) What is the probability of spending less than 9 days in recovery? \r<BR>\n" );
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document.write( "_______%\r<BR>\n" );
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document.write( "b) What is the probability of spending more than 6 days in recovery? \r<BR>\n" );
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document.write( "_______%\r<BR>\n" );
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document.write( "c) What is the probability of spending between 6 days and 9 days in recovery? \r<BR>\n" );
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document.write( "_______% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850009 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve these problems using a graphing calculator:\r<BR>\n" );
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document.write( "**a) Probability of spending less than 9 days in recovery:**\r<BR>\n" );
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document.write( "1.  **Normalcdf function:** We'll use the `normalcdf` function on the calculator. This function calculates the area under a normal distribution curve between a lower and upper bound.\r<BR>\n" );
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document.write( "2.  **Inputs:**<BR>\n" );
document.write( "    *   Lower bound: Since we want the probability of *less* than 9 days, our lower bound can be a very small number (like -10000). This effectively covers the entire left tail of the distribution.<BR>\n" );
document.write( "    *   Upper bound: 9 days<BR>\n" );
document.write( "    *   Mean: 5 days<BR>\n" );
document.write( "    *   Standard deviation: 1.5 days\r<BR>\n" );
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document.write( "3.  **Calculator steps (may vary depending on your calculator model):**<BR>\n" );
document.write( "    *   Press `2nd` then `VARS` to access the `DISTR` menu.<BR>\n" );
document.write( "    *   Select `normalcdf`.<BR>\n" );
document.write( "    *   Enter the values: `normalcdf(-10000, 9, 5, 1.5)`<BR>\n" );
document.write( "    *   Press `ENTER`.\r<BR>\n" );
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document.write( "4.  **Result:** The calculator should give you a result of approximately 0.9962.  Multiply by 100 to express as a percentage: 99.62%.  Rounded to the nearest tenth of a percent, this is **99.6%**.\r<BR>\n" );
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document.write( "**b) Probability of spending more than 6 days in recovery:**\r<BR>\n" );
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document.write( "1.  **Normalcdf function:** We'll use `normalcdf` again.\r<BR>\n" );
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document.write( "2.  **Inputs:**<BR>\n" );
document.write( "    *   Lower bound: 6 days<BR>\n" );
document.write( "    *   Upper bound: A very large number (like 10000) to cover the right tail of the distribution.<BR>\n" );
document.write( "    *   Mean: 5 days<BR>\n" );
document.write( "    *   Standard deviation: 1.5 days\r<BR>\n" );
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document.write( "3.  **Calculator steps:**<BR>\n" );
document.write( "    *   `normalcdf(6, 10000, 5, 1.5)`\r<BR>\n" );
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document.write( "4.  **Result:** The calculator should give you approximately 0.2525 or **25.3%**.\r<BR>\n" );
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document.write( "**c) Probability of spending between 6 days and 9 days in recovery:**\r<BR>\n" );
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document.write( "1.  **Normalcdf function:** Same as before.\r<BR>\n" );
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document.write( "2.  **Inputs:**<BR>\n" );
document.write( "    *   Lower bound: 6 days<BR>\n" );
document.write( "    *   Upper bound: 9 days<BR>\n" );
document.write( "    *   Mean: 5 days<BR>\n" );
document.write( "    *   Standard deviation: 1.5 days\r<BR>\n" );
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document.write( "3.  **Calculator steps:**<BR>\n" );
document.write( "    *   `normalcdf(6, 9, 5, 1.5)`\r<BR>\n" );
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document.write( "4.  **Result:** Approximately 0.7437 or **74.4%**. </SPAN>\n" );
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