document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631182>Question 631182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Americans watch an average of 3.5 hours of television per person per day. If the standard deviation for the number of hours of television watched per day is 3.9 and a random sample of 266 Americans is selected, the mean of this sample belongs to a sampling distribution.\r<BR>\n" );
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document.write( "(a) What is the shape of this sampling distribution?<BR>\n" );
document.write( " (1)skewed right normal <BR>\n" );
document.write( " (2)symmetrical     <BR>\n" );
document.write( " (3)skewed left <BR>\n" );
document.write( " (4)uniform\r<BR>\n" );
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document.write( "(b) What is the mean of this sampling distribution? (Give your answer correct to one decimal place.)\r<BR>\n" );
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document.write( "(c) What is the standard deviation of this sampling distribution? (Give your answer correct to two decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397406 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=397406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) What is the shape of this sampling distribution?\r<BR>\n" );
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document.write( "(1)skewed right normal<BR>\n" );
document.write( "<font color=\"red\">(2)symmetrical</font><BR>\n" );
document.write( "(3)skewed left<BR>\n" );
document.write( "(4)uniform\r<BR>\n" );
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document.write( "Answer choice marked in <font color=\"red\">red</font>.\r<BR>\n" );
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document.write( "This is because the distribution will approach a normal distribution (ie become more like it) as you increase the sample size.<BR>\n" );
document.write( "Remember that normal distributions are symmetrical.\r<BR>\n" );
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document.write( "The other choices that involved the word \"skewed\" are incorrect because skewed is the opposite of symmetrical. So that's out. \r<BR>\n" );
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document.write( "Also, it's not uniform because the more extreme cases (eg: those who watch barely any TV or those who watch too much TV) will not have the same proportion as those who watch the average amount of TV\r<BR>\n" );
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document.write( "(b) What is the mean of this sampling distribution? (Give your answer correct to one decimal place.)\r<BR>\n" );
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document.write( "The mean of the sampling distribution is equal to the population mean. So the mean of this sampling distribution is <font color=\"red\">3.5 hours</font>.\r<BR>\n" );
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document.write( "(c) What is the standard deviation of this sampling distribution? (Give your answer correct to two decimal places.)\r<BR>\n" );
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document.write( "The standard deviation of the sampling distribution with population standard deviation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma ALIGN=MIDDLE  ALT=\"sigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > and size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\" title=\"\LARGE \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\" />\r<BR>\n" );
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document.write( "Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+3.9 ALIGN=MIDDLE  ALT=\"sigma+=+3.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+266 ALIGN=MIDDLE  ALT=\"n+=+266\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE \sigma_{\bar{x}} = \frac{3.9}{\sqrt{266}}\" title=\"\LARGE \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\" />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE \sigma_{\bar{x}} \approx \frac{3.9}{16.3095}\" title=\"\LARGE \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\" />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\LARGE \sigma_{\bar{x}} \approx 0.23912\" title=\"\LARGE \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\" /> \r<BR>\n" );
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document.write( "So the standard deviation of this sampling distribution is approximately <font color=\"red\">0.24</font> (rounded to two decimal places).\r<BR>\n" );
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