document.write( "Question 1188939: A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the boys whose times are among the top (or fastest) 10% with certificates of recognition. What time (in seconds) would the boys need to beat in order to earn a certificate of recognition from the fitness association? Round your answer to one decimal place. \n" ); document.write( "
Algebra.Com's Answer #820227 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the population mean is 440 seconds.
\n" ); document.write( "the population standard deviation is 60 seconds.
\n" ); document.write( "the z-score that has 10% of the area under the normal distribution curve to the left of it is equal to -1.28155 rounded to 5 decimal places.
\n" ); document.write( "the raw score associated with that is based on the z-score formula of:
\n" ); document.write( "z = (x - m) / s
\n" ); document.write( "z is the z-score
\n" ); document.write( "x is the raw score
\n" ); document.write( "m is the mean
\n" ); document.write( "s is the standard deviation.
\n" ); document.write( "the formula becomes:
\n" ); document.write( "-1.28155 = (x - 440) / 60
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = -1.28155 * 60 + 440 = 363.107 seconds
\n" ); document.write( "any times less than that will get the certificate of recognition.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );