To find the area under the standard normal curve between the z-scores of 1.5 and 2.5, you can use the cumulative distribution function (CDF) for the standard normal distribution, which is often represented as Z or Φ(z).
Here’s a step-by-step guide to perform the calculation:
- Find the CDF values: You’ll need to find the cumulative probabilities for both z-scores. This can be done using standard normal distribution tables or a calculator that provides the CDF for normal distributions.
- Look up or calculate the probabilities:
- The CDF value for z = 1.5 is approximately 0.9332.
- The CDF value for z = 2.5 is approximately 0.9938.
- Calculate the area between the two z-scores:
The area under the curve between z = 1.5 and z = 2.5 can be calculated by subtracting the CDF value at z = 1.5 from the CDF value at z = 2.5:
Area = Φ(2.5) – Φ(1.5)
Area ≈ 0.9938 – 0.9332 ≈ 0.0606
- Conclusion: Therefore, the area under the standard normal curve between z = 1.5 and z = 2.5 is approximately 0.0606. This value represents the probability that a standard normal random variable falls between these two z-scores.
If you need a more precise value or wish to explore this further, consider using statistical software or online calculators that handle normal distributions!