document.write( "Question 148383: The mean mass of game fish in a certain locale is determined to be 2.5 kg and the standard deviation is 0.75 kg.\r
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\n" ); document.write( "\n" ); document.write( "b. Suppose a fish with a mass of less than 1.75 kg must be thrown back. What percent of the fish cannot be kept if caught?\r
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Algebra.Com's Answer #108911 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
The mean mass of game fish in a certain locale is determined to be 2.5 kg and the standard deviation is 0.75 kg.
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document.write( "Now we convert everything from from x-scores to z-scores. The x-scores are\r\n" );
document.write( "the actual values of the fishes' mass in kg.  The z-scores will be the\r\n" );
document.write( "coded values of those x-scores.\r\n" );
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document.write( "So we find the z-scores of the x-endpoints of the\r\n" );
document.write( "desired area, 1 and 4, using\r\n" );
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document.write( "\"z=%28x-mu%29%2Fsigma\"\r\n" );
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document.write( "For left endpoint x=1,\r\n" );
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document.write( "\"z=%281-2.5%29%2F0.75=%28-1.5%29%2F0.75=-2\", which\r\n" );
document.write( "means that left endpoint x=1 on the x-axis will \r\n" );
document.write( "corresponds to the new left endpoint z=-2 on the new\r\n" );
document.write( "z-axis.\r\n" );
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document.write( "For right endpoint x=4,\r\n" );
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document.write( "\"z=%284-2.5%29%2F0.75=%281.5%29%2F0.75=2\", which\r\n" );
document.write( "means that right endpoint x=4 on the x-axis will \r\n" );
document.write( "corresponds to the new right endpoint x=2.\r\n" );
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document.write( "Now we take away the x-axis, put in the\r\n" );
document.write( "new z-axis, and move the y-axis to the middle of the graph:\r\n" );
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document.write( "We can find the right half of the area by looking in\r\n" );
document.write( "the table.  Find 2.0 in the z-column and .00 across the\r\n" );
document.write( "top, and we see 0.4772.\r\n" );
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document.write( "By the symmetry of the normal curve, the left half of \r\n" );
document.write( "that area is the same, so we double 0.4772 and the\r\n" );
document.write( "answer is .9544\r\n" );
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document.write( "You can also do the whole thing immediately on a TI-83\r\n" );
document.write( "or TI-84:\r\n" );
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document.write( "Clear the screen\r\n" );
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document.write( "PRESS     2nd VARS 2\r\n" );
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document.write( "you see this on the screen:\r\n" );
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document.write( "                normalcdf(\r\n" );
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document.write( "Then type after it so that you have this on the screen:\r\n" );
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document.write( "                normalcdf(1,4,2.5,.75)\r\n" );
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document.write( "Press ENTER and read  .954499876\r\n" );
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document.write( "Notice that is rounds to .9545, not .9544 as we found\r\n" );
document.write( "using the table in the book, but this can be expected \r\n" );
document.write( "because the table is not as accurate as the calculator. \r\n" );
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\n" ); document.write( "b. Suppose a fish with a mass of less than 1.75 kg must be thrown back. What percent of the fish cannot be kept if caught?
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document.write( "On the graph with the x-axis, we want the area marked A:\r\n" );
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document.write( "It's the area marked A, the area to the left of the point 1.75 on the\r\n" );
document.write( "x-axis that we're looking for.   \r\n" );
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document.write( "So now we 'code' that x-score cut-off point 1.75 as a z-scores, for\r\n" );
document.write( "this is our new cut-off point, x=1.75,\r\n" );
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document.write( "\"z=%281.75-2.5%29%2F0.75=%28-.75%29%2F0.75=-1\", which\r\n" );
document.write( "means that the cut-off point x=1.75 on the x-axis will \r\n" );
document.write( "corresponds to the new cut-off point z=-1 on the new\r\n" );
document.write( "z-axis.\r\n" );
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document.write( "Now we look up z=1.00 in the table and read 0.3413. However that's the\r\n" );
document.write( "area marked B, not the area marked A.  The table only gives the area\r\n" );
document.write( "starting at the middle of the graph (left of the y-axis).\r\n" );
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document.write( "However we know that the whole left side is .5.  So we subtract the area\r\n" );
document.write( "marked B, which is 0.3413, from .5000 and get 0.1587.\r\n" );
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document.write( "So the percent is found by moving the decimal two places right and putting\r\n" );
document.write( "on a percent mark.\r\n" );
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document.write( "Answer:  15.87% of the fish must be thrown back. \r\n" );
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document.write( "As before can also do the whole thing immediately on a TI-83\r\n" );
document.write( "or TI-84:\r\n" );
document.write( " \r\n" );
document.write( "Clear the screen\r\n" );
document.write( " \r\n" );
document.write( "PRESS     2nd VARS 2\r\n" );
document.write( " \r\n" );
document.write( "you see this on the screen:\r\n" );
document.write( "   \r\n" );
document.write( "                normalcdf(\r\n" );
document.write( " \r\n" );
document.write( "Then type after it so that you have this on the screen:\r\n" );
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document.write( "                normalcdf(-99999999,1.75,2.5,0.75) \r\n" );
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document.write( "[that's a negative sign, not a minus sign, located at the very\r\n" );
document.write( " bottom right of the calculator. It looks like this (-).\r\n" );
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document.write( "Press ENTER and read  0.1586552596\r\n" );
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document.write( "which this time rounds to the same answer 0.1587 as when we \r\n" );
document.write( "used the table.  \r\n" );
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document.write( "normalcdf(LEFTBOUND, RIGHTBOUND, MEAN, STANDARDDEVIATION) then press ENTER.\r\n" );
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document.write( "If the area goes all the way to the left, use -99999999 for the LEFTBOUND.\r\n" );
document.write( "If the area goes all the way to the right, use 99999999 for the RIGHTBOUND.\r\n" );
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document.write( "Edwin
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