document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483477>Question 483477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are dashes over the x's I don't know how to start the equations since I know nothing about algebra since I never took it in school.\r<BR>\n" );
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document.write( "Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.\r<BR>\n" );
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document.write( "      	a. Describe the shape of the sampling distribution of the sample mean ×. Do we need to make any assumptions about the shape of the population? Why or why not?\r<BR>\n" );
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document.write( "b. Find the mean and the standard deviation of the sampling distribution of the sample mean ×.<BR>\n" );
document.write( "c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P (× > 21). Hint: Find the z value corresponding to 21 by using µx and &#417;x because we wish to calculate a probability about x. Then sketch the sampling distribution and the probability.\r<BR>\n" );
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document.write( "d. Calculate the probability that we will obtain a sample mean less than 19.385; that is, calculate P (× < 19.385).<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 #330858 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=330858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.<BR>\n" );
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document.write( "a. Describe the shape of the sampling distribution of the sample means ×.<BR>\n" );
document.write( "Ans: Nearly normal according to the Central Limit theorem.<BR>\n" );
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document.write( "Do we need to make any assumptions about the shape of the population? Why or why not?<BR>\n" );
document.write( "Ans: Check the statement of the Central Limit Theorem in your text.<BR>\n" );
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document.write( "b. Find the mean and the standard deviation of the sampling distribution of the sample mean ×.<BR>\n" );
document.write( "mean of the sample means = 20<BR>\n" );
document.write( "std of the sample means = 4/sqrt(64) = 1/2<BR>\n" );
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document.write( "c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P (x-bar > 21). Hint: Find the z value corresponding to 21 by using µx and &#417;x because we wish to calculate a probability about x. Then sketch the sampling distribution and the probability.<BR>\n" );
document.write( "z(21) = (21-20)/[1/2] = 2<BR>\n" );
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document.write( "P(x-bar > 21) = P(z > 2) = 0.0228<BR>\n" );
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document.write( "d. Calculate the probability that we will obtain a sample mean less than 19.385; that is, <BR>\n" );
document.write( "calculate P (x-bar < 19.385)<BR>\n" );
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document.write( "z(19.385) = (19.385-21)/(1/2) = -3.2300<BR>\n" );
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document.write( "P(x-bar < 19.385) = P(z < -3.2300) = 0.00061901<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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