Question C.4: Find the area under the curve that is outside of two standar...
Find the area under the curve that is outside of two standard deviations from the mean.
What the problem is asking for:
(6.4.1)
Appendix B Table A provides the right half of the area between the mean and z = +2. To find the area in the right tail, subtract the amount between the mean and z = +2 from .5000:
(6.4.2)
Area under the right side of the curve: .5000
S ubtract the area from z = 0 to z = +2.00: − .4772
The area to the right of z = +2.00 is: .0228
The same amount will be in each tail, so the total area in both tails is 2(.0228) = .0456.
(6.4.3)
Another way to arrive at the same answer is to note that the area within two standard deviations of the mean is .9544, as shown previously, so the area outside of that is 1.0000 − .9544 = .0456.
