document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128419>Question 1128419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An elevator has a placard stating that the maximum capacity is 1600 lb—10 passengers.&#8203; So, 10 adult male passengers can have a mean weight of up to 1600/10=160 pounds. If the elevator is loaded with 10 adult male&#8203; passengers, find the probability that it is overloaded because they have a mean weight greater than 160 lb.&#8203; (Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb&#8203;.) \r<BR>\n" );
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document.write( "1.The probability the elevator is overloaded is?<BR>\n" );
document.write( "*-Please show work to help me understand-*<BR>\n" );
document.write( "2. Does this elevator appear to be&#8203; safe?<BR>\n" );
document.write( "  A.Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.<BR>\n" );
document.write( "  B. No, 10 randomly selected people will never be under the weight limit.<BR>\n" );
document.write( "  C.Yes, 10 randomly selected people will always be under the weight limit.<BR>\n" );
document.write( "  D.&#8203;No, there is a good chance that 10 randomly selected people will exceed the elevator capacity. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744967 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=744967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> maximum capacity is 1600 pounds.<BR>\n" );
document.write( "maximum number of passengers is 10.\r<BR>\n" );
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document.write( "the mean weight of each passenger is given as 166 pounds with a standard deviation of 29 pounds.\r<BR>\n" );
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document.write( "the 10 passengers are treated as a sample of size 10.<BR>\n" );
document.write( "therefore, you have to use the standard error of the distribution of sample means rather than the standard deviation.\r<BR>\n" );
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document.write( "the formula for standard error is s = standard deviation / square root of sample size.\r<BR>\n" );
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document.write( "this comes out to be s = 29 / sqrt(10) = 9.170605214\r<BR>\n" );
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document.write( "you need to find the z-score.\r<BR>\n" );
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document.write( "the formula for z-score is z = (x-m)/s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the stnadard error of the distribution of sample means.\r<BR>\n" );
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document.write( "plugging in the numbers, you get:\r<BR>\n" );
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document.write( "z = (160 - 166) /. 9.170605214.\r<BR>\n" );
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document.write( "this resuls in z = -.6542643435\r<BR>\n" );
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document.write( "using a z-score calculator to find the area under the normal distribution curve to the right of that z-score, you get an area of .7435293114.\r<BR>\n" );
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document.write( "round to 4 decimal places and it becomes .7435.\r<BR>\n" );
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document.write( "the calculator i used is the TI-84 Plus.\r<BR>\n" );
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document.write( "there is also an online calculator that you can use that does the same thing.\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 using that calculator are shown below:\r<BR>\n" );
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document.write( "using z-scores:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/110907.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "using raw scores:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/110906.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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