document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197675>Question 1197675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, where the amount requested for home loans followed the normal distribution with a mean of $80 000 and a standard deviation of $24 000. (Round z-score computation to 2 decimal places and the final answers to the nearest whole dollars.)\r<BR>\n" );
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document.write( "a. What is the minimum amount requested on the largest 2% of loans?\r<BR>\n" );
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document.write( "b. What is the maximum amount requested on the smallest 10% of loans?\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 #831048 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52799)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The amounts of money requested on home loan applications at Down River Federal Savings <BR>\n" );
document.write( "follow the normal distribution, where the amount requested for home loans followed <BR>\n" );
document.write( "the normal distribution with a mean of $80 000 and a standard deviation of $24 000. \r<BR>\n" );
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document.write( "a. What is the minimum amount requested on the largest 2% of loans?\r<BR>\n" );
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document.write( "b. What is the maximum amount requested on the smallest 10% of loans?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  The normal distribution is a bell-shaped curve.\r\n" );
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document.write( "     In this question, you are given the area under the specified normal distribution curve \r\n" );
document.write( "     on the right of the row z-score of 1-0.02 = 0.98.\r\n" );
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document.write( "     It means that they want you find the value of the inverse accumulated normal distribution function\r\n" );
document.write( "     at the mean value of 80,000, standard deviation of 24,000, and the row z-score of 0.98.\r\n" );
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document.write( "     You may use online free of charge calculator \r\n" );
document.write( "     https://onlinestatbook.com/2/calculators/inverse_normal_dist.html\r\n" );
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document.write( "     It will show you the entire process in visual form, \r\n" );
document.write( "     so you will see and understand what you are doing and you will be able to learn.\r\n" );
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document.write( "        +---------------------------------------------------------------------+\r\n" );
document.write( "        |   Using this online calculator is indispensable as a teaching tool  |\r\n" );
document.write( "        |            for a beginner student to learn the subject.             |\r\n" );
document.write( "        +---------------------------------------------------------------------+\r\n" );
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document.write( "     Alternatively, if you just have some introductory conceptual knowledge, you can use your standard calculator.  \r\n" );
document.write( "     The function to use is invNorm(mean,SD,z).\r\n" );
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document.write( "     If you need instructions for it, you can find them in the internet at this link\r\n" );
document.write( "     https://www.youtube.com/watch?v=RPzxs-Hd8s0   (video-lesson for Casio calculators)  or\r\n" );
document.write( "     https://www.youtube.com/watch?v=7mkfGJO8ehM   (video-lesson for TI-83 or TI-84)     or\r\n" );
document.write( "     https://cosmosweb.champlain.edu/people/stevens/WebTech/TIFiles/Chap6-TI-83.pdf (textual description).\r\n" );
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document.write( "     The answer is $129,290   (rounded).\r\n" );
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document.write( "(b)  The normal distribution is a bell-shaped curve.\r\n" );
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document.write( "     In this question, you are given the area under the specified normal distribution curve \r\n" );
document.write( "     on the left of the row z-score of 0.10.\r\n" );
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document.write( "\r\n" );
document.write( "     It means that they want you find the value of the inverse accumulated normal distribution function\r\n" );
document.write( "     at the mean of 80,000, standard deviation of 24,000, and the row z-score of 0.10.\r\n" );
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document.write( "\r\n" );
document.write( "     It will show you the entire process in visual form, \r\n" );
document.write( "     so you will see and understand what you are doing and you will be able to learn.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        +---------------------------------------------------------------------+\r\n" );
document.write( "        |   Using this online calculator is indispensable as a teaching tool  |\r\n" );
document.write( "        |            for a beginner student to learn the subject.             |\r\n" );
document.write( "        +---------------------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Alternatively, if you just have some introductory conceptual knowledge, you can use your standard calculator. \r\n" );
document.write( "     The function to use is invNorm(mean,SD,z).\r\n" );
document.write( "\r\n" );
document.write( "     If you need instructions on how to use it, you can find them in the internet at this link\r\n" );
document.write( "     https://www.youtube.com/watch?v=RPzxs-Hd8s0   (video-lesson for Casio calculators)  or\r\n" );
document.write( "     https://www.youtube.com/watch?v=7mkfGJO8ehM   (video-lesson for TI-83 or TI-84)     or\r\n" );
document.write( "     https://cosmosweb.champlain.edu/people/stevens/WebTech/TIFiles/Chap6-TI-83.pdf (textual description).\r\n" );
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document.write( "     The answer is $49,243   (rounded).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Let me explain my teaching conception about this subject.\r<BR>\n" );
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document.write( "I assume that there are two major different reasons why visitors come to this forum <BR>\n" );
document.write( "with such problems/questions.\r<BR>\n" );
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document.write( "One reason is when they want simply get the number/(the answer) without any learning.\r<BR>\n" );
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document.write( "It is a sad case, but it is still a real life.  Such visitors do not need any teaching/explanations, at all.\r<BR>\n" );
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document.write( "The other reason is when the visitors still want to learn.\r<BR>\n" );
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document.write( "As a rule, such beginner visitors don't know what the problem really wants from them; <BR>\n" );
document.write( "don't know how to approach, don't know what to do, and don't know how to do.\r<BR>\n" );
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document.write( "For such beginner visitors, I strongly recommend to start with the online solver/calculator.<BR>\n" );
document.write( "It provides a visual support, which works better than any teacher.<BR>\n" );
document.write( "In addition, this visual support prevents you from making errors.<BR>\n" );
document.write( "After inputting, it shows the area of interest as a shaded area, so you can see what you do.\r<BR>\n" );
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document.write( "After playing with this solver/calculator 3-5-10 times, you will understand the subject enough<BR>\n" );
document.write( "to make your further calculations using your standard calculator.\r<BR>\n" );
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document.write( "After that, you may use your standard calculator as your basic tool, and you can practice <BR>\n" );
document.write( "with it to prepare yourself for exam.\r<BR>\n" );
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document.write( "After that, you may use the online calculator for the checking purposes, only.\r<BR>\n" );
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document.write( "It is a solid way for beginners to become a professional master in the field and then teach others.\r<BR>\n" );
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