document.write( "Question 1186253: The scores on a national achievement exam are normally distributed with a mean of 500 and a standard deviation of 100. If a student who took the exam is randomly selected, find the probability that the student scored below 600. Assume a normal distribution. \n" ); document.write( "
Algebra.Com's Answer #849355 by ikleyn(52813)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( "The scores on a national achievement exam are normally distributed with a mean of 500 \n" ); document.write( "and a standard deviation of 100. If a student who took the exam is randomly selected, \n" ); document.write( "find the probability that the student scored below 600. Assume a normal distribution. \n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "Notice that 600 is one standard deviation from the mean 500.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "According to the empirical rule, 68% of all scores are within one standard deviation \r\n" ); document.write( "from the mean.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Due to the symmetry of normal curve, it means that half of that, or 34% of all scores \r\n" ); document.write( "are in the interval [500,600].\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Add to it 50% of scores that are under the mean, and you will get the ANSWER\r\n" ); document.write( "to the problem's question of 50% + 34% = 84%.\r\n" ); document.write( "\r \n" ); document.write( "\n" ); document.write( "Solved.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |