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Potassium blood levels in healthy humans are normally distributed with a mean of 17.0 mg/100 ml, and standard deviation of 1.0 mg/100 ml. Elevated
levels of potassium indicate an electrolyte balance problem, such as may be caused by Addison’s disease. However, a test for potassium level should not cause too many “false positives”. What level of potassium should we use so that only 2.5 % of healthy individuals are classified as “abnormally high”?
Use normal distribution
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The phrase "normally distributed" should give a clue as to the use of Z-score table and the z-score equation which is:

You're given the standard deviation, mean and means to find the z-score.

1. You know that your data needs to exclude 2.5% of the population which means you're looking for 97.5% (0.975) look this up on your table and you get 1.96.

So now that you rearrange the equation so that x is the subject of the formula.

the answer that you get should be 18.96 mg/ 100 mL.

by Wooden (489 points)

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