Fishi Posted August 10, 2007 Share Posted August 10, 2007 Two different groups of test-takers received scores on the GXYZ standardized test. Group A''s scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B''s scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?a) 1/9 b) 1/8 c) 1/6 d) 4/17 e) 4/21 Can anybody tell me how to solve this? Thanks!:tup: Quote Link to comment Share on other sites More sharing options...
cooldude929 Posted August 10, 2007 Share Posted August 10, 2007 Is the answer 1/9 ? Here is what I came up with: Group A: Mean 460, SD =20 ,Example series: 400,420,440,460,480,500,520 Group A: Mean 520, SD =40 ,Example series: 400,440,480,520,560,600,640 Here I have taken example series of 7 numbers in each.. these series statisfy Mean and SD. Now, lets get to the point. only 400 is less than 440 in Series B. Total is 14. => 1/7 ( not given in answers). If I take another no# on both sides for each series it becomes 2/18 =>1/9.. So answer can be any one of the following series : 1/7,1/9,3/22, 4/26... 1/9 suits in our case Quote Link to comment Share on other sites More sharing options...
cooldude929 Posted August 10, 2007 Share Posted August 10, 2007 I know my approach is dirty.. Any smart ideas ? Quote Link to comment Share on other sites More sharing options...
kundan77 Posted August 11, 2007 Share Posted August 11, 2007 In a normally distributed data, about 68% of the values are within one standard deviation (SD) of the mean, about 95% of the values are within 2SD and about 99.7 % lie within 3SD. Group A has mean of 460 and SD of 20, so one who scored less than 440 lies 1SD away from mean = (100-68)/2 = 16% Group B has mean of 520 and SD of 40, so one who scored less than 440 lies 2SD away from mean = (100-95)/2 = 2.5% Fraction of total test-takers from Group-B who scored less than 440 = 2.5/(2.5+16) = 2.5/18.5 can be approximated to 1/7.4 => answer: 1/8 Quote Link to comment Share on other sites More sharing options...
Fishi Posted August 12, 2007 Author Share Posted August 12, 2007 The answer is 1/9. You will come up with this if you take for the first standard deviation 68% and for the second 96%. But nevertheless THANK YOU VERY MUCH[clap] Quote Link to comment Share on other sites More sharing options...
openeye Posted August 12, 2007 Share Posted August 12, 2007 there should also be a thread with more detailed explanations here somewhere Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.