document.write( "Question 1172479: The heights of applicants to the police force are normally distributed with mean 170 cm and standard deviation 3.8 cm. If 30% applicants are rejected on account of their low height. What is the minimum acceptable height for the police force? \n" ); document.write( "
Algebra.Com's Answer #797520 by Theo(13342)\"\" \"About 
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mean is 170 cm.
\n" ); document.write( "standard deviation is 3.8 cm.
\n" ); document.write( "30% are rejected.
\n" ); document.write( "minimal height is 168.007 cm.
\n" ); document.write( "anybody shorter than that is rejected.
\n" ); document.write( "i used the following calculator to find this.
\n" ); document.write( "http://davidmlane.com/hyperstat/z_table.html
\n" ); document.write( "here's a display of the results.
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\n" ); document.write( "if you had to use the z-score tables you would do the following.
\n" ); document.write( "look for an area to the left of the z-score that is closest to .30
\n" ); document.write( "i round:
\n" ); document.write( ".30153 associated with a z-score of -.52
\n" ); document.write( ".29806 associated with a z-score of -.53.
\n" ); document.write( "the difference between the two z-scores is .01
\n" ); document.write( "the difference between the two areas is .00347
\n" ); document.write( "the difference between .30153 and .3 is .00153.
\n" ); document.write( ".00153 / .00347 = x / .01
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = .0044092219.
\n" ); document.write( "subtract this from -.52 to get -.5244092219.
\n" ); document.write( "in the z-score formula of:
\n" ); document.write( "z = (x - m) / s
\n" ); document.write( "z = -.5244092219
\n" ); document.write( "m = 170
\n" ); document.write( "s = 3.8
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 3.8 * -.5244092219 + 170 = 168.007245.
\n" ); document.write( "that 's very close to what the calculator told me.
\n" ); document.write( "that's your solution.
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