Final answer:
To find the percent of observations from a standard normal distribution that satisfies each statement, use the standard normal distribution table or a calculator to find the areas associated with the given z-scores. Then, subtract the areas from 1 and multiply by 100 to find the percentages.
Step-by-step explanation:
To find the percent of observations from a standard normal distribution that satisfies each statement, we can use the standard normal distribution table or a calculator. The z-score is the number of standard deviations that a data point is from the mean. For example, for z > 1.68, we can find the area to the right of 1.68 on the standard normal distribution table or use a calculator to find the corresponding percentage. Similarly, for z < 1.68, we can find the area to the left of 1.68. For z > -0.96, we find the area to the right of -0.96, and so on.
The percentages can be found by subtracting the area from 1 and multiplying by 100. For example, if the area to the right of 1.68 is 0.0461, then the percentage is (1 - 0.0461) * 100 = 95.39%. Similarly, for z < 1.68, if the area to the left is 0.4539, then the percentage is 0.4539 * 100 = 45.39%.
The percentages for the given statements are as follows:
- z > 1.68: 100 - 4.61 = 95.39%
- z < 1.68: 45.39%
- z > -0.96: 100 - 83.72 = 16.28%