Question

Find the​ z-scores that separate the middle ​85% of the distribution from the area in the tails of the standard normal distribution.

what are the z scores?

Answer 1

-1.44

+1.44

Explanation:

You want the z-scores that bracket the middle 85% of a normal distribution.

Lower tail

The lower tail will have half the area of the remaining part of the distribution:

(1 -0.85)/2 = 0.075

The z-score associated with this area is about -1.43953147094, approximately -1.44.

The distribution is symmetrical, so the middle 85% will be bracketed by the z-scores -1.44 and +1.44.

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Additional comment

The attached calculator display shows these scores give the middle 85.01% of the distribution.

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