document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=584836>Question 584836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is from a normal distribution chapter: Not sure if I use the central limit theorem. Can anyone walk me through it? Trying to learn how to find the right clues to do problems such as these.\r<BR>\n" );
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document.write( "Assume that a lifetime (in hrs) of a particular type of transistor battery is approximately mound shaped, not necessarily normal, with a mean of 100 hrs and standard deviation of 20 hrs.<BR>\n" );
document.write( "a) What proportion of the batteries will last between 100 and 115 hrs?<BR>\n" );
document.write( "b) Within what limits around the  population mean will 90% of the samples fall? Min____  Max_____?<BR>\n" );
document.write( "c) If a random sample of 49 batteries is selected, what \"proportion\" of sample means will be between 100 and 115 hrs? (THIS THROWS ME off since I thought proportions were done later with confidence intervals..?)<BR>\n" );
document.write( "d) If a random sample of 25 batteries is selected, what proportion of sample means will be between 100 and 115 hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373017 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=373017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that a lifetime (in hrs) of a particular type of transistor battery is approximately mound shaped, not necessarily normal, with a mean of 100 hrs and standard deviation of 20 hrs.<BR>\n" );
document.write( "a) What proportion of the batteries will last between 100 and 115 hrs?<BR>\n" );
document.write( "z(100) = 0<BR>\n" );
document.write( "z(115) = (115-100)/20 = 15/20 = 3/4<BR>\n" );
document.write( "P(100< x <115) = P(0< z <3/4) = normalcdf(0,3/4) = 0.2734<BR>\n" );
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document.write( "b) Within what limits around the population mean will 90% of the samples fall?<BR>\n" );
document.write( "Find the z-value with a left-tail of 0.05: -1.645<BR>\n" );
document.write( "Then the z-value with a right-tail of 0.05 is: +1.645<BR>\n" );
document.write( "Min = -1.645*20 + 100 = 67.1<BR>\n" );
document.write( "Max = +1.645*20 + 100 = 132.9<BR>\n" );
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document.write( "c) If a random sample of 49 batteries is selected, what \"proportion\" of sample means will be between 100 and 115 hrs? (THIS THROWS ME off since I thought proportions were done later with confidence intervals..?)<BR>\n" );
document.write( "z(100) = 0<BR>\n" );
document.write( "z(115) = (115-100)/[20/sqrt(49)] = 5.25<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(100< x-bar <115) = P(0< z < 5.25) = 0.5000<BR>\n" );
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document.write( "d) If a random sample of 25 batteries is selected, what proportion of sample means will be between 100 and 115 hours?<BR>\n" );
document.write( "z(100) = 0<BR>\n" );
document.write( "z(115) = (115-100)/[20/sqrt(25)] = 15/(20/5) = 15/4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(100< x-bar <115) = P(0< z <15/4) = 0.4999<BR>\n" );
document.write( "==============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===============<BR>\n" );
document.write( " </SPAN>\n" );
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