What is the lowest z-value for the highest 2% of observations on the standard normal distribution?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.02) and its Z score.

To find the lowest z-value for the highest 2% of observations on the standard normal distribution, we need to find the z-value that corresponds to the cumulative area of 0.98 (1 - 0.02).

To calculate this, you can use a standard normal distribution table, also known as the Z-table. This table provides the cumulative area under the standard normal curve for different z-values.

1. Begin by finding the closest value to 0.98 in the body of the Z-table. In this case, the closest value is 0.9798.

2. Next, identify the corresponding z-value for the closest value in the body of the table. In this case, the corresponding z-value is 2.05.

Therefore, the lowest z-value for the highest 2% of observations on the standard normal distribution is approximately -2.05 (since the standard normal distribution is symmetrical).

Note: You can also use statistical software or calculators to find the z-value directly by entering the cumulative area of 0.98 or using the inverse normal distribution function.