document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203243>Question 1203243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to solve this problem, thank you!\r<BR>\n" );
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document.write( "The average age of a vehicle registered in Canada is about 100 months and the standard deviation for the population is 19..\r<BR>\n" );
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document.write( "If a random sample of 33 vehicles is selected, find the probability (as percent) that the mean of their age is between 105 and 107 months.\r<BR>\n" );
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document.write( "The probability is:    %<BR>\n" );
document.write( "(Round your answer to the nearest whole percent) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838648 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean of population is 100 months.<BR>\n" );
document.write( "standard deviation of population is  19.<BR>\n" );
document.write( "sample size is 33<BR>\n" );
document.write( "since you are looking for the mean of the sample, use the standard error rather than the standard devition.<BR>\n" );
document.write( "standard error = standard deviation / square root of sample size = 19 / sqrt(33) = 3.3075.<BR>\n" );
document.write( "you want to know the probability that the mean age is between 105 and 107 months.<BR>\n" );
document.write( "since you have the standard deviastion of the population, use the z-score.<BR>\n" );
document.write( "that formula is z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the popultion mean.<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "for x = 105, the formula becomes z = (105 - 100) / 3.3075 = 1.626.<BR>\n" );
document.write( "for x = 107, the formula becomes z = (107 - 100) / 3.3075 = 2.276.<BR>\n" );
document.write( "the area to the left of z = 1.626 = .9480<BR>\n" );
document.write( "the area to the left of z = 2.276 = .9886<BR>\n" );
document.write( "the area in between is the larger area minus the smaller area = .0406.<BR>\n" );
document.write( "that's the probability of getting a z-score between 1.6726 and 2.276.<BR>\n" );
document.write( "that is also the probability of getting an average age between 105 and 107.\r<BR>\n" );
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document.write( "using the z-score calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>, this is what the output looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/081011.jpg\">\r<BR>\n" );
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document.write( "you could use the z-score tables, but the use of the calculator is easier and allows for greater accuracy. </SPAN>\n" );
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