document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181223>Question 1181223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The random variable x represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850070 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=850070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You haven't provided the data (the number of credit cards adults have and their corresponding probabilities).  I need that information to calculate the mean and standard deviation.  However, I can give you the formulas and explain the process.\r<BR>\n" );
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document.write( "**Let's say you have the following data (replace these with your actual data):**\r<BR>\n" );
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document.write( "| Number of Credit Cards (x) | Probability P(x) |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| 0 | 0.10 |<BR>\n" );
document.write( "| 1 | 0.35 |<BR>\n" );
document.write( "| 2 | 0.30 |<BR>\n" );
document.write( "| 3 | 0.20 |<BR>\n" );
document.write( "| 4 | 0.05 |\r<BR>\n" );
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document.write( "**1. Calculate the Mean (μ):**\r<BR>\n" );
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document.write( "The mean (or expected value) is calculated as:\r<BR>\n" );
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document.write( "μ = Σ [x * P(x)]\r<BR>\n" );
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document.write( "This means you multiply each value of x by its corresponding probability and then add up all those products.\r<BR>\n" );
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document.write( "Using our example data:\r<BR>\n" );
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document.write( "μ = (0 * 0.10) + (1 * 0.35) + (2 * 0.30) + (3 * 0.20) + (4 * 0.05)<BR>\n" );
document.write( "μ = 0 + 0.35 + 0.60 + 0.60 + 0.20<BR>\n" );
document.write( "μ = 1.75\r<BR>\n" );
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document.write( "**2. Calculate the Variance (σ²):**\r<BR>\n" );
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document.write( "The variance is calculated as:\r<BR>\n" );
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document.write( "σ² = Σ [(x - μ)² * P(x)]\r<BR>\n" );
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document.write( "This means you subtract the mean from each value of x, square the result, multiply by the corresponding probability, and then add up all those products.\r<BR>\n" );
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document.write( "Using our example data:\r<BR>\n" );
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document.write( "σ² = (0 - 1.75)² * 0.10 + (1 - 1.75)² * 0.35 + (2 - 1.75)² * 0.30 + (3 - 1.75)² * 0.20 + (4 - 1.75)² * 0.05<BR>\n" );
document.write( "σ² = 3.0625 * 0.10 + 0.5625 * 0.35 + 0.0625 * 0.30 + 1.5625 * 0.20 + 5.0625 * 0.05<BR>\n" );
document.write( "σ² = 0.30625 + 0.196875 + 0.01875 + 0.3125 + 0.253125<BR>\n" );
document.write( "σ² = 1.0875\r<BR>\n" );
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document.write( "**3. Calculate the Standard Deviation (σ):**\r<BR>\n" );
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document.write( "The standard deviation is simply the square root of the variance:\r<BR>\n" );
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document.write( "σ = √σ²\r<BR>\n" );
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document.write( "Using our example data:\r<BR>\n" );
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document.write( "σ = √1.0875<BR>\n" );
document.write( "σ ≈ 1.04\r<BR>\n" );
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document.write( "**Provide your data, and I'll calculate the mean and standard deviation for you.**<BR>\n" );
document.write( " </SPAN>\n" );
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