Final answer:
To find the area under the standard normal curve to the left of specified Z-scores, reference the appropriate value in a Z-table. If the table does not cover specific Z-scores, utilize statistical software or calculators. The area to the right is found by subtracting the area to the left from 1, and the area between two Z-scores is the difference in their corresponding cumulative probabilities.
Step-by-step explanation:
To determine the area under the standard normal curve to the left of the given Z-scores, we utilize a Z-table which displays the cumulative probability from the far left of the distribution up to a given Z-score. For each Z-score, one must look up the corresponding area under the curve in the Z-table. However, if we do not have specific Z-scores available from a given Z-table, we would typically use statistical software or a calculator with statistical functions to find the associated area.
For the Z-scores given, (a) Z=0.84, (b) Z=0.64, (c) Z=0.94, (d) z=0.83, the process would be to look up each of these Z-scores in the Z-table and record the corresponding probability which represents the area under the curve to the left of each Z-score. To illustrate, if using a Z-table that shows the cumulative area left of Z=1.5 to be 0.9332, we could find similarly formatted data for our Z-scores mentioned.
To determine the probability to the right of a Z-score, subtract the area to the left from 1, remembering that the total area under a normal distribution is always 1. When seeking to assess the area between two Z-scores, subtract the smaller cumulative probability from the larger one.