document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615851>Question 615851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6.The scores for an admissions test have a mean of 1200 with a standard deviation of 60. A random sample of 64 scores is selected and the sample mean is calculated.\r<BR>\n" );
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document.write( "a)The sample mean is Normally distributed. What are the mean and the standard deviation for the distribution of the sample mean?<BR>\n" );
document.write( "b)What is the probability that the sample mean will be larger than 1205?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387351 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=387351\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The scores for an admissions test have a mean of 1200 with a standard deviation of 60. A random sample of 64 scores is selected and the sample mean is calculated. <BR>\n" );
document.write( "a)The sample mean is Normally distributed. What are the mean and the standard deviation for the distribution of the sample mean?<BR>\n" );
document.write( "The Central Limit Theorem says:<BR>\n" );
document.write( "The mean of the sample means = the mean of the population: 1200<BR>\n" );
document.write( "The std of the sample means = 60/sqrt(64) = 60/8 = 7.5<BR>\n" );
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document.write( "b)What is the probability that the sample mean will be larger than 1205?<BR>\n" );
document.write( "z(1205) = (1205-1200)/7.5 = 2/3<BR>\n" );
document.write( "P(x-bar > 1205) = P(z > 2/3) = normalcdf(2/3,100) = 0.2525<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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