document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=444206>Question 444206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Any help you can give me on these problems will be greatly appreciated.\r<BR>\n" );
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document.write( "1)<BR>\n" );
document.write( "The new Twinkle bulb has a standard deviation 35 hours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be 500 hours. \r<BR>\n" );
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document.write( "(a.	Find the margin of error E for a 95% confidence interval. Round your answer to the nearest hundredths. <BR>\n" );
document.write( "(b.	Construct a 95% confidence interval for the mean life, mu of all Twinkle bulbs.\r<BR>\n" );
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document.write( "2) A standard placement test has a mean of 115 and a standard deviation of &#61555; = 10. Determine the minimum sample size if we want to be 95% certain that we are within 3 points of the true mean. \r<BR>\n" );
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document.write( "3)An experimental egg farm is raising chickens to produce low cholesterol eggs. A lab tested 16 randomly selected eggs and found that the mean cholesterol was 190 mg with a standard deviation of 18.0 mg. Assume that the population is normally distributed. \r<BR>\n" );
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document.write( "a.	What is the margin of error for a 95% confidence interval? Round your answer to the nearest tenths. <BR>\n" );
document.write( "b.	What is the 95% confidence interval for the population mean cholesterol content for all experimental eggs? Assume that the population is normally distributed. \r<BR>\n" );
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document.write( "4.	The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 100 of these new bulbs is selected from the production line. It was found that 64 lasted more than 1000 hours. \r<BR>\n" );
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document.write( "a.	What is the margin of error (E)? Round to the nearest three decimals. <BR>\n" );
document.write( "b.	What is the 95% confidence interval for the population proportion (p) of all Twinkle bulbs? \r<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 #306274 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=306274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Any help you can give me on these problems will be greatly appreciated.<BR>\n" );
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document.write( "All of your problems are essentially the same.<BR>\n" );
document.write( "You need a \"sample mean\"(x-bar) and you need a \"margin of error\"(ME).<BR>\n" );
document.write( "The sample mean is provided by the problem narrative.<BR>\n" );
document.write( "The ME = z*s/sqrt(n) where z depends on the level of confidence,<BR>\n" );
document.write( "s is the standeard deviation (usually given) and n is the sample size.<BR>\n" );
document.write( "The Confidence Interval is (x-bar - ME) < u < (x-bar + ME)<BR>\n" );
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document.write( "1)<BR>\n" );
document.write( "The new Twinkle bulb has a standard deviation 35 hours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be 500 hours. <BR>\n" );
document.write( "(a. Find the margin of error E for a 95% confidence interval. Round your answer to the nearest hundredths.<BR>\n" );
document.write( "ME = z*s/sqrt(n)<BR>\n" );
document.write( "ME = 1.96*35/sqrt(50) = 9.7015<BR>\n" );
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document.write( "(b. Construct a 95% confidence interval for the mean life, mu of all Twinkle bulbs.<BR>\n" );
document.write( "500-9.7015 < u < 500+9.7015<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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