The area under the standard normal distribution curve between z = 1.50 and z = 2.50 can be calculated using the cumulative distribution function (CDF) for the standard normal distribution.
To find the area, you need to look up the z-scores in the standard normal distribution table (or use a calculator). The CDF gives you the probability that a standard normal random variable is less than or equal to a certain z-score.
1. **Find the CDF values**:
- For z = 1.50, the CDF is approximately 0.9332.
- For z = 2.50, the CDF is approximately 0.9938.
2. **Calculate the area between the two z-scores**:
Subtract the CDF value of the lower z-score from the CDF value of the upper z-score:
Area = CDF(2.50) – CDF(1.50) = 0.9938 – 0.9332 = 0.0606.
This means that the area, or the probability, of a value falling between z = 1.50 and z = 2.50 in a standard normal distribution is approximately 0.0606, or 6.06%.