Final answer:
To find areas under the normal curve corresponding to z-scores using the Z-table, locate the cumulative area to the left for each z-score. For negative scores, these areas will be smaller, and to find areas to the right or between scores, 1 is subtracted from the area to the left or differences are taken, respectively.
Step-by-step explanation:
The question asks to use the Z-table to find the area under the normal curve to the left of specified z-scores. The areas to the left of z-scores represent the cumulative probability up to that z-score on a standard normal distribution curve. Using the Z-table:
- For z=0.55, look up the corresponding cumulative area in the Z-table.
- For z=1.33, find its cumulative area in the Z-table.
- For negative z-scores such as z=-1.05, z=-2.18, and z=-2.57, the process is the same but keep in mind that these will have smaller cumulative areas due to their location on the left side of the mean on the normal curve.
To calculate the area to the right of a z-score, subtract the area to the left from 1. For example:
- If the Z-table shows the area to the left of z=0.55 as 0.6554, the area to the right is 1 - 0.6554 = 0.3446.
To find the area between two z-scores, subtract the cumulative area of the lower z-score from that of the higher z-score. For instance, if the area to the left of z=1.5 is 0.9332 and z=-0.40 is 0.3446, then the area between them is 0.9332 - 0.3446 = 0.5886.