document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=757283>Question 757283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 40 cars is to be selected for a speed study.<BR>\n" );
document.write( "A) What are the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 40?<BR>\n" );
document.write( "Shape is normal, mean of the sample means=67 mph, std of the sample means of the size 40 6/ (sqrt <BR>\n" );
document.write( "B) What is the probability that the sample mean will be 69 miles per hour or more?<BR>\n" );
document.write( "C) What is the probability that the sample mean will be between 65 and 68 miles per hour?<BR>\n" );
document.write( "D) What is the probability that the sample mean will be less than 66 miles per hour?<BR>\n" );
document.write( "2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 200 adults is to be selected to test this claim.<BR>\n" );
document.write( "A) What are the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of 200?<BR>\n" );
document.write( "B) What is the probability that the sample proportion will fall within 0.02 of the population proportion?<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 #460727 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=460727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 40 cars is to be selected for a speed study.<BR>\n" );
document.write( "A) What are the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 40?<BR>\n" );
document.write( "Shape is normal, mean of the sample means=67 mph, std of the sample means of the size 6/sqrt(40)<BR>\n" );
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document.write( "B) What is the probability that the sample mean will be 69 miles per hour or more?<BR>\n" );
document.write( "z(69) = (69-67)/[6/sqrt(40)]= 2.1082<BR>\n" );
document.write( "P(x-bar >= 69) = P(z >= 2.1082) = 0.0175<BR>\n" );
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document.write( "C) What is the probability that the sample mean will be between 65 and 68 miles per hour?<BR>\n" );
document.write( "Find the z-value of 65 and of 68<BR>\n" );
document.write( "Find the probability z is between those z-values.<BR>\n" );
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document.write( "D) What is the probability that the sample mean will be less than 66 miles per hour?<BR>\n" );
document.write( "Use the same process as with \"a\" and \"b\".<BR>\n" );
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document.write( "2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 200 adults is to be selected to test this claim.<BR>\n" );
document.write( "A) What are the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of 200?<BR>\n" );
document.write( "normal; mean = 0.35 ; std = sqrt[0.35*0.65/200] = 0.0337<BR>\n" );
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document.write( "B) What is the probability that the sample proportion will fall within 0.02 of the population proportion?<BR>\n" );
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document.write( "Find the z value that is 2% above the mean.<BR>\n" );
document.write( "invNorm(0.52) = 0.0502<BR>\n" );
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document.write( "So the z-values that are 2% above and below the mean are +-0.0502<BR>\n" );
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document.write( "Use x = z*s+u to find the corresponding proportions:<BR>\n" );
document.write( "x = 0.0502*0.03370 + 0.35 = 0.3517<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = -0.0502*0.03370 + 0.35 = 0.3483<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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