Question

An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of 570 and a standard deviation of 125. The individuals who exceed 750 on this test are considered to be potential leaders. What proportion of the population are considered to be potential leaders? Round your answer to at least four decimal places, 5 ?

Answer 1

X-4 750 – 570 180 2 – score for 750 is – o 125 125 = 1.44 Proportion of population are considered to be potential leaders is Pr(X > 750) = Pr(z > 1.44) = 1 - 0.9251 = 0.0749

lz 0.00 0.01 0.02 0.03 0.04 | 0.0 05 0.504 0.508 0.512 0.516 01 0.5398 0.5438 0.5478 0.5517 0.5557 02 0.5793 0.5832 0.5871 0.591 0.5948 03 0.6179 0.6217 0.6255 0.6293 06331 10.4 0.6554 0.6591 06628 0.6664 0.67 10.5 0.6915 0.695 0.6985 0.7019 0.7054 10.6 0.7257 0.7291 0.7324 0.7357 07389 0.7 0.758 0.7611 0.7642 07673 07704 10.8 0.7881 0.791 07939 0.7967 07995 0.9 0.8159 0.8186 0.8212 0.8238 08264. 1.0 0.8413 0.8438 08461 08485 0.8508 11 08643 0.8665 0.8686 08708 08729 12 0.8849 0.8869 0.8888 08907 08925 13 09032 09049 0.9066 0.9082 0.9099 1.4 09192 09207 09222 09236 0.9251