3 For a standard normal curve find the zscores for the follo

3. For a standard normal curve, find the z-score(s) for the following: 3A. The area to the left is 0.2005.

–0.84

–2.05

+0.84

+2.05

3B. The area to the right is 0.3483.

–0.39

–0.36

+0.39

+0.36

3C. The area to the left is 0.8508.

–1.04

+1.04

–0.15

+0.15

3D. The area to the right is 0.7517.

+0.43

–2.95

–0.68

+1.43

3E. The lower and upper z-scores for the middle 0.7994.

–0.84, +0.84

–0.21, +0.21

–1.12, 1.12

–1.28, +1.28

Solution

a)

Using a table/technology,

z = -0.84 [answer]

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b)

Here, thus, the area to the left is 1 - 0.3483 = 0.6517.

Using a table for this left tailed area,

z = 0.39 [answer]

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c)

Using a table/technology,

z = 1.04 [answer]

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d)

Here, thus, the area to the left is 1 - 0.7517 = 0.2483.

Using a table for this left tailed area,

z = -0.68 [answer]

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e)

This is the middle 0.7994, so each extreme tail has an area (1-0.7994)/2 = 0.1003.

Thus,

z = -1.28, and its positive counterpart, +1.28. [This argument is by symmetry of the normal curve]