document.write( "Question 78749This question is from textbook Elementary Statistics
\n" ); document.write( ": Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3,000. If a teacher is seledcted at random, find the probability that he or she makes more than $36,000. \n" ); document.write( "

Algebra.Com's Answer #56496 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Assume that the salaries of elementary school teachers in the United States are
\n" ); document.write( "normally distributed with a mean of $32,000 and a standard deviation of $3,000.
\n" ); document.write( "If a teacher is seledcted at random, find the probability that he or she makes
\n" ); document.write( "more than $36,000.\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "I'm sorry that statistics course are in a \r\n" );
document.write( "confusing state of transition between the\r\n" );
document.write( "two types of tables and the use of the\r\n" );
document.write( "technology, and that you are a victim of\r\n" );
document.write( "circumstances. \r\n" );
document.write( "\r\n" );
document.write( "It depends on what textbook you are using and whether \r\n" );
document.write( "your teacher is old-fashioned or modern.  Different \r\n" );
document.write( "textbooks have different kinds of normal distribution \r\n" );
document.write( "tables.  Some teachers require you to use tables and \r\n" );
document.write( "others allow you to use a graphing calculator such as \r\n" );
document.write( "the TI-83 or TI-84.\r\n" );
document.write( "\r\n" );
document.write( "I'll try to cover all three methods below:\r\n" );
document.write( "\r\n" );
document.write( "The answer by calculator is .0912112819. The\r\n" );
document.write( "answer by tables is .0918. The table is not\r\n" );
document.write( "as accurate as the calculator.\r\n" );
document.write( "\r\n" );
document.write( "Here's how to find that on a TI-83 or TI-84.\r\n" );
document.write( "\r\n" );
document.write( "normalcdf(36000,1E99,32000,3000)\r\n" );
document.write( "\r\n" );
document.write( "Then press ENTER. You will get the answer\r\n" );
document.write( ".0912112819.\r\n" );
document.write( "\r\n" );
document.write( "Here's how to do that on your TI calculator:\r\n" );
document.write( "\r\n" );
document.write( "To get:\r\n" );
document.write( "\r\n" );
document.write( "normalcdf(\r\n" );
document.write( "\r\n" );
document.write( "1. press 2ND \r\n" );
document.write( "2. press VARS\r\n" );
document.write( "3. press 2\r\n" );
document.write( "\r\n" );
document.write( "There is a key for the comma just above the\r\n" );
document.write( "7 key. To get E (for exponent) press 2ND and \r\n" );
document.write( "then the comma key.\r\n" );
document.write( "\r\n" );
document.write( "If you are required to use the tables, then \r\n" );
document.write( "you calculate the z-score for the left bound\r\n" );
document.write( "x = 36000:\r\n" );
document.write( "\r\n" );
document.write( "     x - m\r\n" );
document.write( "z = -------\r\n" );
document.write( "      s/Ön\r\n" );
document.write( "\r\n" );
document.write( "where m = 32000, s = 3000, n = 1. (There is only one \r\n" );
document.write( "teacher in the sample.)\r\n" );
document.write( "\r\n" );
document.write( "z-score for 36000 is calculated thusly:\r\n" );
document.write( "\r\n" );
document.write( "     36000 - 32000\r\n" );
document.write( "z = --------------- = 1.333333333 \r\n" );
document.write( "        3000/Ö1\r\n" );
document.write( "        \r\n" );
document.write( "To use tables you will have to round that off\r\n" );
document.write( "to 1.33 \r\n" );
document.write( "\r\n" );
document.write( "Some tables have negative numbers and\r\n" );
document.write( "and some don't.\r\n" );
document.write( "\r\n" );
document.write( "If your table has negative z-scores,\r\n" );
document.write( "then you will look up the area to the left\r\n" );
document.write( "of 1.33 and find it to be .9082.\r\n" );
document.write( "\r\n" );
document.write( "So you will subtract 1 - .9082 and get .0918\r\n" );
document.write( "\r\n" );
document.write( "If your table does not have negative z-scores\r\n" );
document.write( "then you ignore the sign, look up 1.33, and \r\n" );
document.write( "find .4082. Then you must subtract that from\r\n" );
document.write( ".5000 and get .5000-.4082 = .0918.\r\n" );
document.write( " \r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );