The area under the standard normal distribution curve between two z-scores can be found using statistical tables or a standard normal distribution calculator. In this case, we want to find the area between z = 0 and z = 2.16.
Here’s a step-by-step guide on how to calculate this area:
- Understand the Standard Normal Distribution: The standard normal distribution is a bell-shaped curve that represents the distribution of a variable. The total area under this curve is equal to 1.
- Identify the z-scores: We have two z-scores: z = 0 (the mean) and z = 2.16.
- Use the Standard Normal Distribution Table: You can look up the z-scores in a standard normal distribution table (Z-table) to find the corresponding areas. For z = 0, the area to the left is 0.5000. For z = 2.16, the area to the left is approximately 0.9846.
- Calculate the Area Between the Two z-scores: To find the area between z = 0 and z = 2.16, subtract the area at z = 0 from the area at z = 2.16:
Area = P(Z < 2.16) - P(Z < 0)
Area = 0.9846 – 0.5000 = 0.4846
Thus, the area under the standard normal distribution curve between z = 0 and z = 2.16 is approximately 0.4846, or 48.46%. This means that about 48.46% of the data falls between these two z-scores in a standard normal distribution.