document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204070>Question 1204070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manufacturer knows that their items have a normally distributed lifespan with a mean of 15 years in standard deviation of 3.6 years. If you randomly purchase one item, what is the probability that it will last longer than 20 years. Round answer to 2 decimal places.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840142 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "mu = 15 = mean<BR>\n" );
document.write( "sigma = 3.6 = standard deviation\r<BR>\n" );
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document.write( "Compute the z score when x = 20<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (20-15)/(3.6)<BR>\n" );
document.write( "z = 1.38888888888889<BR>\n" );
document.write( "z = 1.39\r<BR>\n" );
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document.write( "The task of computing P(X > 20) is approximately the same as finding P(Z > 1.39)\r<BR>\n" );
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document.write( "Use a Z table found in the back of your stats textbook. <BR>\n" );
document.write( "The table should look like the one found here<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a><BR>\n" );
document.write( "Scroll down to the row that starts with \"+1.3\"<BR>\n" );
document.write( "Then look at the column that has \"0.09\" at the top<BR>\n" );
document.write( "The intersection of the row and column yields the approximate value 0.91774\r<BR>\n" );
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document.write( "This will indicate that P(Z < 1.39) = 0.91774 approximately.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "P(Z > 1.39) = 1 - P(Z < 1.39)<BR>\n" );
document.write( "P(Z > 1.39) = 1 - 0.91774<BR>\n" );
document.write( "P(Z > 1.39) = 0.08226\r<BR>\n" );
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document.write( "This leads us back to P(X > 20) = 0.08226 when mu = 15 and sigma = 3.6\r<BR>\n" );
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document.write( "There's about a 8.226% chance of selecting a item that will last longer than 20 years.\r<BR>\n" );
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document.write( "If you want to use a TI83 or TI84, then check out this article<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.statology.org/normal-probabilities-ti-84-calculator/\">https://www.statology.org/normal-probabilities-ti-84-calculator/</a><BR>\n" );
document.write( "The input will be <font color=red>normalcdf(20,9999,15,3.6)</font><BR>\n" );
document.write( "The 9999 represents a very large upper bound to basically represent positive infinity. <BR>\n" );
document.write( "The result of this calculation is approximately 0.0824333239 which isn't far off from the previous result we got (0.08226)\r<BR>\n" );
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document.write( "Here's another calculator you can use<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://davidmlane.com/normal.html\">https://davidmlane.com/normal.html</a><BR>\n" );
document.write( "That calculator provides a diagram as well.<BR>\n" );
document.write( "The result from that calculator should be 0.0824\r<BR>\n" );
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document.write( "When rounding to two decimal places, it leads to <font color=red size=4>0.08</font> as the final answer.<BR>\n" );
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