document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132829>Question 1132829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this​ information, answer the following questions.What proportion of light bulbs will last more than 61 ​hours?<BR>\n" );
document.write( "​(b) What proportion of light bulbs will last 52 hours or​ less?<BR>\n" );
document.write( "​(c) What proportion of light bulbs will last between 57 and 62 ​hours?<BR>\n" );
document.write( "​(d) What is the probability that a randomly selected light bulb lasts less than 46 ​hours </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749969 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=749969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 57 hours.<BR>\n" );
document.write( "standard deviation is 3.5 hours.\r<BR>\n" );
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document.write( "use the z-score to find the answer you need.<BR>\n" );
document.write( "formula for z-score is z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw score mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "(a) what proportion of light bulbs will last more than 61 hours.\r<BR>\n" );
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document.write( "z = (61 - 57) / 3.5 = 1.142857143.<BR>\n" );
document.write( "area to the right of that z-score is equal to .1265490059.<BR>\n" );
document.write( "that's the probability of the life of the light bulb to be greater than 61.\r<BR>\n" );
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document.write( "​(b) What proportion of light bulbs will last 52 hours or​ less?\r<BR>\n" );
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document.write( "z = (52 - 57) / 3.5 = -1.428571429<BR>\n" );
document.write( "area to the left of that z-score is equal to .0765637714.<BR>\n" );
document.write( "that's the probability of the life of the light bulb to be less than 52.\r<BR>\n" );
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document.write( "​(c) What proportion of light bulbs will last between 57 and 62 ​hours?\r<BR>\n" );
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document.write( "the z-score for 57 is equal to (57 - 57) / 3.5 = 0<BR>\n" );
document.write( "the z-score for 62 is equal to (62 - 57) / 3.5 = 1.428571429<BR>\n" );
document.write( "the area to the left of a z-score of 0 is equal to .5<BR>\n" );
document.write( "the area to the left of a z-score of 1.428571429 is equal to .9234362286.<BR>\n" );
document.write( "the area between a z-score of 0 and a z-score of 1.428571429 is equal to .9234362286 minus .5 = .4234362286.<BR>\n" );
document.write( "that's the probability of the life of the light bulb to be between 57 and 62 hours.\r<BR>\n" );
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document.write( "​(d) What is the probability that a randomly selected light bulb lasts less than 46 ​hours\r<BR>\n" );
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document.write( "z = (46 - 57) / 3.5 = -3.142857143.<BR>\n" );
document.write( "the area to the left of that z-score is equal to .0008366040026.<BR>\n" );
document.write( "round to 2 decimal places and it becomes 0.\r<BR>\n" );
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document.write( "i used the TI-84 Plus calculator to get the answers.\r<BR>\n" );
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document.write( "you can also use the z-score tables, but your z-score would need to be rounded to 2 decimal digits.\r<BR>\n" );
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document.write( "the z-score table gives you the area to the left of the z-score.<BR>\n" );
document.write( "to get the area to the right of the z-score, you would need to take 1 minus the area to the left of the z-score.\r<BR>\n" );
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document.write( "there is an online calculator that can also do this directly from the mean and the standard deviation of the raw score as well as from the z-score.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "the results from the use of that calculator, in the order that the the problems were presented, is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011601.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011602.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011603.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011604.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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