document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170930>Question 1170930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6 days and standard deviation of 1.7 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 6 days in recovery?  % <BR>\n" );
document.write( "b) What is the probability of spending more than 4 days in recovery?  % <BR>\n" );
document.write( "c) What is the probability of spending between 4 days and 6 days in recovery?  % <BR>\n" );
document.write( "Question Help Question 4:  Video 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851062 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=851062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem using the properties of a normal distribution:\r<BR>\n" );
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document.write( "**Understanding the Problem**\r<BR>\n" );
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document.write( "* We have a normal distribution.<BR>\n" );
document.write( "* Mean (μ) = 6 days<BR>\n" );
document.write( "* Standard deviation (σ) = 1.7 days\r<BR>\n" );
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document.write( "**Using a Graphing Calculator**\r<BR>\n" );
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document.write( "Most graphing calculators (like TI-84, etc.) have built-in functions to calculate probabilities for normal distributions. Here's the general process:\r<BR>\n" );
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document.write( "1.  **Access the Normal Distribution Function:**<BR>\n" );
document.write( "    * Look for a \"DISTR\" or \"Distribution\" menu.<BR>\n" );
document.write( "    * Find \"normalcdf\" (normal cumulative distribution function).\r<BR>\n" );
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document.write( "2.  **Input the Values:**<BR>\n" );
document.write( "    * `normalcdf(lower_bound, upper_bound, mean, standard_deviation)`\r<BR>\n" );
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document.write( "**Calculations**\r<BR>\n" );
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document.write( "**a) Probability of spending less than 6 days in recovery**\r<BR>\n" );
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document.write( "* We want P(X < 6), where X is the recovery time.<BR>\n" );
document.write( "* `lower_bound`: A very small number (e.g., -1E99 or -10000) to represent negative infinity.<BR>\n" );
document.write( "* `upper_bound`: 6<BR>\n" );
document.write( "* `mean`: 6<BR>\n" );
document.write( "* `standard_deviation`: 1.7\r<BR>\n" );
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document.write( "    * `normalcdf(-1E99, 6, 6, 1.7)`<BR>\n" );
document.write( "    * The result will be approximately 0.5\r<BR>\n" );
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document.write( "* Percentage: 0.5 \* 100% = 50.0%\r<BR>\n" );
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document.write( "**b) Probability of spending more than 4 days in recovery**\r<BR>\n" );
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document.write( "* We want P(X > 4)<BR>\n" );
document.write( "* `lower_bound`: 4<BR>\n" );
document.write( "* `upper_bound`: A very large number (e.g., 1E99 or 10000)<BR>\n" );
document.write( "* `mean`: 6<BR>\n" );
document.write( "* `standard_deviation`: 1.7\r<BR>\n" );
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document.write( "    * `normalcdf(4, 1E99, 6, 1.7)`<BR>\n" );
document.write( "    * The result will be approximately 0.88079\r<BR>\n" );
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document.write( "* Percentage: 0.88079 \* 100% ≈ 88.1%\r<BR>\n" );
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document.write( "**c) Probability of spending between 4 days and 6 days in recovery**\r<BR>\n" );
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document.write( "* We want P(4 < X < 6)<BR>\n" );
document.write( "* `lower_bound`: 4<BR>\n" );
document.write( "* `upper_bound`: 6<BR>\n" );
document.write( "* `mean`: 6<BR>\n" );
document.write( "* `standard_deviation`: 1.7\r<BR>\n" );
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document.write( "    * `normalcdf(4, 6, 6, 1.7)`<BR>\n" );
document.write( "    * The result will be approximately 0.38079\r<BR>\n" );
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document.write( "* Percentage: 0.38079 \* 100% ≈ 38.1%\r<BR>\n" );
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document.write( "**Answers**\r<BR>\n" );
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document.write( "* a) 50.0%<BR>\n" );
document.write( "* b) 88.1%<BR>\n" );
document.write( "* c) 38.1% </SPAN>\n" );
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