SOLUTION: 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 580 and a standard de

Question 136093: 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 580 and a standard deviation of 125 . The individuals who exceed 780 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.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 580 and a standard deviation of 125 . The individuals who exceed 780 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.
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Draw a picture of a normal curve on a horizontal axis.
Put mean=580 at the middle.
Mark 780 at an appropriate point.
You want the area to the right of 780
normalcdf(780,1000,580,125) = 0.0544 is the answer using a TI calculator.
If you don't have a calculator:
z(780)=(780-580)/125 = 1.6
P(780 < x < 1000) = P(1.6 < z < 10) = 0.0548
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The calculator gives these answers that differ in the 4th decimal.
You might want to use whatever chart you have for your course to
decide which answer you want to use.
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Cheers,
Stan H.

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