To find the area under the standard normal curve between z = 0 and z = 3, we can use the standard normal distribution table, often called the Z-table. This table provides the area (or probability) to the left of a given z-score.
First, we look up the z-score of 0 in the Z-table. The area to the left of z = 0 is 0.5000, meaning that 50% of the data under the curve lies below this point.
Next, we look up the z-score of 3. The Z-table typically shows that the area to the left of z = 3 is approximately 0.9987. This means that nearly 99.87% of the data lies below this z-score.
To find the area between z = 0 and z = 3, we need to subtract the area at z = 0 from the area at z = 3:
Area between z = 0 and z = 3 = Area(z = 3) – Area(z = 0)
Area = 0.9987 – 0.5000 = 0.4987
Thus, the area under the standard normal curve between z = 0 and z = 3 is approximately 0.4987, which is about 49.87% of the total area under the curve.