Sure, I'd be happy to help you with that!
To find P(-1.00 ≤ z), we need to use the standard normal (z-score) table. This table provides the probability of a standard normal distribution up to a certain z-value.
1. Start by opening the standard normal (z-score) table. You can find this table in many statistics textbooks or online resources.
2. Locate the row in the table that corresponds to the first digit of the z-value. In this case, the first digit of -1.00 is -1.0. Find the row that starts with -1.0.
3. Move along the row to find the column that corresponds to the second digit of the z-value. In this case, the second digit of -1.00 is 0.0. Find the column that starts with 0.0.
4. The cell at the intersection of the row and column will give you the probability up to that z-value. In this case, the cell will give you the probability up to -1.00.
5. Read the value in the cell. This will be the probability P(-1.00 ≤ z).
For the second part of your question, to find the probability that a data value picked at random from a normal population will have a standard score (z) that lies between the z-values 0 and 2.10:
1. Open the standard normal (z-score) table again.
2. Locate the row that corresponds to the first z-value, which is 0.0.
3. Move along the row to find the column that corresponds to the second z-value, which is 2.10.
4. The cell at the intersection of the row and column will give you the probability between those two z-values.
5. Read the value in the cell. This will be the probability that a data value picked at random from a normal population will have a standard score (z) between 0 and 2.10.
Remember, the standard normal (z-score) table provides probabilities up to a given z-value. If you need to find the probability beyond a certain z-value, you may need to use complementary probabilities or interpolation techniques.