document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132991>Question 1132991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An elevator has a placard stating that the maximum capacity is 1256 lblong dash8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1256 divided by 8 equals 157 pounds. If the elevator is loaded with 8 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb.​ (Assume that weights of males are normally distributed with a mean of 161 lb and a standard deviation of 25 lb​.) Does this elevator appear to be​ safe?\r<BR>\n" );
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document.write( "The probability the elevator is overloaded is?\r<BR>\n" );
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document.write( "A.<BR>\n" );
document.write( "​Yes, 8 randomly selected people will always be under the weight limit.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "​No, 8 randomly selected people will never be under the weight limit.<BR>\n" );
document.write( "C.<BR>\n" );
document.write( "​Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity.<BR>\n" );
document.write( "D.<BR>\n" );
document.write( "​No, there is a good chance that 8 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 #750158 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=750158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the average weight of males is 161 pounds with a standard deviation of 25 pounds.\r<BR>\n" );
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document.write( "that's your population if i understand it correctly.\r<BR>\n" );
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document.write( "you choose 8 men randomly from this population.\r<BR>\n" );
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document.write( "you want to know the probability that this sample of 8 men chosen randomly from the population will have a mean weight greater than 157 pounds.\r<BR>\n" );
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document.write( "mean of the sample is 161 pounds.<BR>\n" );
document.write( "standard error of the sample of 8 males is 25 / sqrt(8).<BR>\n" );
document.write( "z-score of the sample is z = (157 - 161) / (25 / sqrt(8)) = -4 / 8.838834765 = -.45254834<BR>\n" );
document.write( "the probability of a sample of 8 men having a z-score greater than -.45254834 is equal to .6745629783.\r<BR>\n" );
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document.write( "your selection is D.<BR>\n" );
document.write( "there's a good chance that 8 randomly selected males will exceed the elevator capacity.\r<BR>\n" );
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document.write( "visually, your distribution looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the shaded area is the area under the normal distribution curve where the mean of your randomly selected 8 people is greater than 157.\r<BR>\n" );
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document.write( "note that the standard error is not the same as the standard deviation.<BR>\n" );
document.write( "the standard deviation is for a sample of one person.<BR>\n" );
document.write( "the standard error is for a sample of more than one person.<BR>\n" );
document.write( "it is the standard deviation of the mean of that sample of more than one person.<BR>\n" );
document.write( "the larger the sample size, the smaller the standard error.<BR>\n" );
document.write( " </SPAN>\n" );
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