document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193306>Question 1193306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A brisk walk at a 6 km per hour, burns an average of 300 calories per hour. If the standard deviation of the distribution is 8 calories, find the probability that a person who walks an hour at the rate of 6 kilometers per hour will burn the following calories.<BR>\n" );
document.write( "A.Less than 294 calories \r<BR>\n" );
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document.write( "B.Between 278 and 318 calories </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848848 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</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=848848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Define Variables**\r<BR>\n" );
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document.write( "* Let X be the random variable representing the number of calories burned per hour.<BR>\n" );
document.write( "* X follows a normal distribution with:<BR>\n" );
document.write( "    * Mean (μ) = 300 calories<BR>\n" );
document.write( "    * Standard deviation (σ) = 8 calories\r<BR>\n" );
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document.write( "**2. Standardize the Values**\r<BR>\n" );
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document.write( "* We'll use the z-score formula: <BR>\n" );
document.write( "    * z = (X - μ) / σ\r<BR>\n" );
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document.write( "**A. Less than 294 calories**\r<BR>\n" );
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document.write( "* Calculate the z-score for X = 294:<BR>\n" );
document.write( "    * z = (294 - 300) / 8 = -0.75\r<BR>\n" );
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document.write( "* Find the probability:<BR>\n" );
document.write( "    * P(X < 294) = P(Z < -0.75) <BR>\n" );
document.write( "    * Using a standard normal distribution table or a calculator, we find P(Z < -0.75) ≈ 0.2266\r<BR>\n" );
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document.write( "* **Therefore, the probability of burning less than 294 calories is approximately 0.2266 (or 22.66%).**\r<BR>\n" );
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document.write( "**B. Between 278 and 318 calories**\r<BR>\n" );
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document.write( "* Calculate the z-scores for X = 278 and X = 318:<BR>\n" );
document.write( "    * z1 = (278 - 300) / 8 = -2.75<BR>\n" );
document.write( "    * z2 = (318 - 300) / 8 = 2.25\r<BR>\n" );
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document.write( "* Find the probability:<BR>\n" );
document.write( "    * P(278 < X < 318) = P(-2.75 < Z < 2.25) <BR>\n" );
document.write( "    * P(-2.75 < Z < 2.25) = P(Z < 2.25) - P(Z < -2.75)\r<BR>\n" );
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document.write( "    * Using a standard normal distribution table or a calculator:<BR>\n" );
document.write( "        * P(Z < 2.25) ≈ 0.9878<BR>\n" );
document.write( "        * P(Z < -2.75) ≈ 0.0030\r<BR>\n" );
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document.write( "    * P(-2.75 < Z < 2.25) ≈ 0.9878 - 0.0030 = 0.9848\r<BR>\n" );
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document.write( "* **Therefore, the probability of burning between 278 and 318 calories is approximately 0.9848 (or 98.48%).**<BR>\n" );
document.write( " </SPAN>\n" );
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