Z-scores have an equivalent percent of the area under the normal circulation curve.

You are watching: X~n(2.9, 0.78). find the z-score corresponding to an observation of 1.5.

While this table might look exceptionally long and also confmaking use of to understand also, it is actually pretty simple! This objective of this table is to convert your z-score into its identical portion.

Your z-score is located on the farthest left yellow column #(3.2)# The yellow row on top is if you have a z-score through a hundreths worth, which you execute. #(0.04)#

First, uncover the row through the z-score #3.2#. (It"s the 3rd row from the bottom.)

Next off, look under the column #0.04#.

Third, uncover where the row and also column intersect! It need to satisfy up at #.4994#.

However, this is just the area in between the halfway allude of the normal circulation curve and your z-score.

Because you desire everything to the appropriate of #-3.24#, you must additionally include #.5# to compensate for the various other 50% of the graph.

#.4994 + .5#

Michelle
Jun 23, 2017

.9994 or 99.94%

Explanation:

If you have actually a graphing calculator, you can use it to discover the location.

Hit second > VARS > 2: normalcdf(

This will certainly prompt you for the lower bound, top bound, mean (#mu#), and traditional deviation (#sigma#).

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First, fill in your reduced and top bounds. You desire to find the area to the right of z = -3.24, which suggests -3.24 and also every little thing over that. Therefore,

lower bound = -3.24top bound = 999

Keep #mu# (the mean) as 0 and #sigma# (the traditional deviation) as 1, given that we are managing z scores.

Then push paste and also enter, and also you should get a solution of approximately .9994, or 99.94%.