Final answer:
To find the area to the right of a z-score in a standard normal distribution, subtract the area to the left (found in a z-table) from 1, as the total area under the curve represents the total probability.
Step-by-step explanation:
Understanding the Standard Normal Distribution
The question involves the standard normal distribution, which is a normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1. The areas under this curve correspond to probabilities related to z-scores. A z-score is a measure of how many standard deviations an element is from the mean. To find the area to the right of a given z-score in a standard normal distribution, you subtract the area to the left of the z-score (found in the z-table) from 1. This is because the total area under the curve is 1, which represents the total probability.
For example, if the area to the left of a z-score is given as 0.9332, the area to the right is calculated as follows:
- Area to the right = 1 - Area to the left
- Area to the right = 1 - 0.9332
- Area to the right = 0.0668
This process can be used to calculate probabilities for various z-scores in a standard normal distribution. The z-score corresponding to a particular percentile can be found using the inverse of the standard normal distribution or a z-table.