An aptitude test is designed to measure leadership abilities

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 $\"An$ and a standard deviation of $\"\"$ . The individuals who exceed $\"\"$ 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.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as

x = critical value =    750
u = mean =    570

s = standard deviation =    125

Thus,

z = (x - u) / s =    1.44

Thus, using a table/technology, the right tailed area of this is

P(z >   1.44   ) =    0.0749337 [ANSWER]

An aptitude test is designed to measure leadership abilities

Solution

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