Appendix B has a table of areas for upper tail z values. I\'m not a big fan of d

Question

Appendix B has a table of areas for upper tail z values. I'm not a big fan of displaying z values like this but since this is our text, we'll make the best of it.

Lower tail areas: All z values below the mean will be negative. So if I had a z value of -1.20, I would look up positive z value of 1.20 on the table (0.3849) and subtract from 0.5000 to give me a lower tail area of 0.1151 or 11.51%.

Upper tail areas: Since the z tables accumulate area from left to right, let's say I want the upper tail area when z=1.96. If I look up 1.96 on the table (0.4750) and then subtract this from 0.5000, I get an upper tail area of 0.025 or 2.5%.

Pick a postive and negative z value (any one), and use Appendix B table to find the corresponding lower and upper tail areas.

Explanation / Answer

Say we pick z = -1.23 and z = 1.23.

For z = -1.23, LEFT TAILED AREA:

Lower tail areas: All z values below the mean will be negative. So if I had a z value of -1.23, I would look up positive z value of 1.23 on the table (0.3907) and subtract from 0.5000 to give me a lower tail area of 0.1093 or 10.93%. [ANSWER]

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For z = -1.23, RIGHT TAILED AREA:

To get the right tailed area, we simply get the complement of the left tailed area,

1 - 0.1093 = 0.8907 [ANSWER]

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For z = 1.23, RIGHT TAILED AREA:

Upper tail areas: Since the z tables accumulate area from left to right, let's say I want the upper tail area when z=1.23. If I look up 1.23 on the table (0.3907) and then subtract this from 0.5000, I get an upper tail area of 0.1093 or 10.93%.

*******************************

For z = 1.23, LEFT TAILED AREA:

To get the left tailed area, we simply get the complement of the right tailed area,

1 - 0.1093 = 0.8907 [ANSWER]

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