Pregunta
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Find the Z-score such that the area under the standard normal curve to the right is 0.20 .
Click the icon to view a table of areas under the normal curve.
The approximate Z-score that corresponds to a right tail area of 0.20 is
(Round to two decimal places as needed.)

Ask by Wells Wells. in the United States
Mar 29,2025

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The approximate Z-score is 0.84.

Solución

We need to find the value of for which the area under the standard normal curve to the right is 0.20. This means that the area to the left of is
Thus, we are looking for the -score such that

Step 1: Use the Standard Normal Table

Look up the probability in the standard normal table to find the corresponding -score. You will find that the -score that gives an area close to to its left is approximately . (More precisely, some tables might show because the exact area for is around , which is close enough for rounding to two decimal places.)

Step 2: Conclude the Answer

Thus, the approximate -score corresponding to a right tail area of 0.20 is

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The Deep Dive

To find the Z-score corresponding to an area of 0.20 to the right, you can look up the value in a Z-table. Since the Z-table typically provides the area to the left of the Z-score, you’ll need to subtract 0.20 from 1, giving you an area of 0.80 to the left. Upon consulting the Z-table, you’ll find that the Z-score that corresponds to an area of 0.80 is approximately 0.84. Thus, the Z-score is about 0.84 when rounded to two decimal places.
To ensure accuracy when looking up values, remember that Z-tables can differ slightly by design, so it’s always a good idea to double-check your Z-score calculations with a reliable source or even a calculator that provides Z-scores and tail areas directly. This way, you can avoid any potential discrepancies!

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