SOLUTION: To qualify for special training, athletes are tested for endurance. The scores are normally distributed with a mean of 840 and a standard deviation of 89. If only the top 15% of

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Question 1200844: To qualify for special training, athletes are tested for endurance.
The scores are normally distributed with a mean of 840 and a standard
deviation of 89. If only the top 15% of the athletes are selected, what would
the cutoff score be?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
top 15% would be those with scores above 932.243.
calculator i used can be found at https://davidmlane.com/hyperstat/z_table.html
here's a display of the results.


if you use z-cores, you would do the followng.
the z-score with 15% of the area under the normnal distribution cure to the right of it is equal to 1.03643338.
z-score formuls is z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation
formula becomes 1.03643338 = (x - 840) / 89.
solve for x to get x = 89 * 1.03643338 + 840 = 923.2425708.
round to 923.243 as shown in the calculator.