Summary
Highlights
The video begins by explaining how to find the area under the normal curve between Z=0 (the mean) and a positive Z-score. For example, to find the area between Z=0 and Z=0.74, locate 0.7 in the Z-table's rows and 0.04 in the columns. The intersection, 0.2704, is the area, as the table's area measurements start from the mean.
Next, the video demonstrates how to find the area between Z=0 and a negative Z-score, such as Z=-1.21. When dealing with negative Z-scores, ignore the negative sign for table lookup. Find the area for Z=1.21 (1.2 in rows, 0.01 in columns), which is 0.3869. This value represents the area between the mean and -1.21.
To find the area to the right of Z=1.27, first find the area between Z=0 and Z=1.27 using the table (1.2 in rows, 0.07 in columns), which is 0.3980. Since the total area of half the curve is 0.5, subtract the found area from 0.5 (0.5 - 0.3980 = 0.102) to get the area to the right.
For the area to the left of Z=-1.32, locate the area between Z=0 and Z=1.32 (ignoring the negative sign). This is 0.4066. Similar to the previous example, subtract this value from 0.5 (0.5 - 0.4066 = 0.0934) to find the area to the left of -1.32.
To find the area between two negative Z-scores, such as Z=-2.15 and Z=-1.47, first find the area from the mean to each Z-score. For Z=-2.15, the area is 0.4842. For Z=-1.47, the area is 0.4292. Subtract the smaller area from the larger area (0.4842 - 0.4292 = 0.055) to get the area between them.
When finding the area between Z=-0.72 and Z=1.35, calculate the area from the mean to each Z-score separately. The area from the mean to -0.72 is 0.2642, and the area from the mean to 1.35 is 0.4115. Add these two areas together (0.2642 + 0.4115 = 0.6757) to find the total area between them.
Finally, to find the area to the right of Z=-0.90, first determine the area from the mean to -0.90, which is 0.3159. Since the area of half the curve is 0.5, add this area to 0.5 (0.5 + 0.3159 = 0.8159) to get the area to the right of -0.90.