document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199258>Question 1199258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. An elevator has a placard stating that the maximum capacity is 3800 lb — 26 passengers.​ So, 26 adult male passengers can have a mean weight of up to 3800/26=146 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 31 lb.<BR>\n" );
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document.write( "a. Find the probability that 1 randomly selected adult male has a weight greater than 146 lb.\r<BR>\n" );
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document.write( "b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 146 lb.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833048 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=833048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 26<BR>\n" );
document.write( "maximum capacity is 3800 pounds<BR>\n" );
document.write( "maximum mean weight of 26 passengers is 3800 / 26 = 146 pounds.<BR>\n" );
document.write( "weight of males is normally distributed with a mean of 185 pounds and a standard deviation of 31 pounds.<BR>\n" );
document.write( "z-score formula is z = (x - m) / s<BR>\n" );
document.write( "x is the weight of an individual or the mean weight of a number of individuals.<BR>\n" );
document.write( "m is the mean weight to test against.<BR>\n" );
document.write( "s the standard deviation if one individual is tested or the standard error if the mean of a number of individuals is tested.\r<BR>\n" );
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document.write( "when checking the weight of an individual, use the standard deviation of the population of men.<BR>\n" );
document.write( "z = (x - m) / s becomes z = (146 - 185) / 31<BR>\n" );
document.write( "x is the weight you want to test against the mean = 146<BR>\n" );
document.write( "m is the mean of the weight of men = 185<BR>\n" );
document.write( "s is the standard deviation of the weight of men = 31<BR>\n" );
document.write( "solve for z to get z = -1.25806 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "since you want to know the probability that a man weighs more than 146 pounds, you are looking for the area to the right of that z-score.\r<BR>\n" );
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document.write( "you can use a z-score calculator to find that.<BR>\n" );
document.write( "i used the ti-84 plus calculator.\r<BR>\n" );
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document.write( "an online calculator that can also be used is at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "using my ti-84 plus, i get the area to the right of a z-score of -1.25806 = .8958 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "the online calculator does the same thing, only rounds differently form some values.\r<BR>\n" );
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document.write( "the result of using that calculator with the z-score is shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/121601.jpg\"><BR>\n" );
document.write( "the result of using that calculator with the raw score is shown below.<BR>\n" );
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document.write( "when you are looking at the mean of a sample of a number of individuals, you use the standard error.<BR>\n" );
document.write( "the standard error is equal to the standard deviation / the square root of the sample size.<BR>\n" );
document.write( "in this problem, the sample size is 26 individuals whose mean weight is 185 and whose standard deviation is 31.<BR>\n" );
document.write( "the standard error is equal to 31 / sqrt(26) = 6.0796 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "z = (146 - 185) / 6.0796 in this case.<BR>\n" );
document.write( "146 is the weight you are testing against.<BR>\n" );
document.write( "185 is the meaan weight of men.<BR>\n" );
document.write( "6.0796 is the standard error.<BR>\n" );
document.write( "the z-score is equal to -6.4149 rounded to 4 decimal places.<BR>\n" );
document.write( "the probability of the mean of all men being greater than 146 pounds is equal to  .99999...... when i use my ti-84 plus calculator.<BR>\n" );
document.write( "that's very very close to 100%.<BR>\n" );
document.write( "the online calculator shows 1 which is equal to 100%.\r<BR>\n" );
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document.write( "the result of using that calculator with the z-score is shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/121603.jpg\"><BR>\n" );
document.write( "the result of using that calculator with the raw score is shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/121604.jpg\">\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo<BR>\n" );
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