document.write( "Question 78633This question is from textbook Elementary Statistics
\n" ); document.write( ": Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches. \n" ); document.write( "
Algebra.Com's Answer #56384 by Edwin McCravy(20054)\"\" \"About 
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Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches.
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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" );
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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" );
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document.write( "I'll try to cover all three methods below:\r\n" );
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document.write( "The answer by calculator is .9811659853. The\r\n" );
document.write( "answer by tables is .9812\r\n" );
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document.write( "Here's how to find that on a TI-83 or TI-84.\r\n" );
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document.write( "normalcdf(63,65,63.6,2.5/Ö(75))\r\n" );
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document.write( "Then press ENTER. You will get the above answer\r\n" );
document.write( "immediately.\r\n" );
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document.write( "Here's how to get that on your TI calculator:\r\n" );
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document.write( "To get:\r\n" );
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document.write( "normalcdf(\r\n" );
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document.write( "1. press 2ND \r\n" );
document.write( "2. press VARS\r\n" );
document.write( "3. press 2\r\n" );
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document.write( "There is a key for the comma just above the 7 key.\r\n" );
document.write( "The square root Ö( is gotten by pressing 2ND then x²\r\n" );
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document.write( "If you are required to use the tables, then first you\r\n" );
document.write( "must calculate the z-scores for the left and right \r\n" );
document.write( "bounds  x = 53 and x = 65 by the formula:\r\n" );
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document.write( "     x - m\r\n" );
document.write( "z = -------\r\n" );
document.write( "      s/Ön\r\n" );
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document.write( "where m = 63.6, s = 2.5, n = 75.\r\n" );
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document.write( "z-score for 63 is calculated thusly:\r\n" );
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document.write( "     63 - 63.6\r\n" );
document.write( "z = ----------- = -2.078460969 \r\n" );
document.write( "      2.5/Ö75\r\n" );
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document.write( "To use tables you will have to round that off\r\n" );
document.write( "to -2.08 \r\n" );
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document.write( "and the z-score for 65: \r\n" );
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document.write( "     65 - 63.6\r\n" );
document.write( "z = ----------- = 4.849742261 \r\n" );
document.write( "      2.5/Ö75\r\n" );
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document.write( "You would round that off to 4.85\r\n" );
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document.write( "But that will be too large to be on any table.\r\n" );
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document.write( "Some tables have negative numbers and\r\n" );
document.write( "and some don't.\r\n" );
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document.write( "If your table has negative z-scores, then:\r\n" );
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document.write( "then you will take the area to the left of \r\n" );
document.write( "4.85 to be 1.\r\n" );
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document.write( "Then you will look up the area to the left\r\n" );
document.write( "of -2.08 and find it to be .0188.\r\n" );
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document.write( "So you will subtract 1 - .0188 and get .9812\r\n" );
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document.write( "If your table does not have negative z-scores\r\n" );
document.write( "then you ignore the sign, look up 2.08, and \r\n" );
document.write( "find .4812. Then you must add .5 to that and \r\n" );
document.write( "get .9812.\r\n" );
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document.write( "Edwin
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