To find the area under the standard normal distribution curve between z = 2.16 and z = 0, we first need to determine the cumulative distribution function (CDF) values for these z-scores. The area under the curve corresponds to the probability of a standard normal variable falling between these two z-scores.
1. **Cumulative Probability for z = 2.16:** According to standard normal distribution tables or using a calculator, the cumulative probability (area to the left) for z = 2.16 is approximately 0.9846.
2. **Cumulative Probability for z = 0:** The cumulative probability for z = 0 is 0.5, as this is the mean of the distribution.
3. **Calculating the Area:** To find the area between z = 2.16 and z = 0, we subtract the cumulative probability at z = 0 from that at z = 2.16:
Area = P(Z < 2.16) - P(Z < 0)
Area = 0.9846 – 0.5 = 0.4846
Therefore, the area under the standard normal distribution curve between z = 2.16 and z = 0 is approximately 0.4846, or 48.46%. This represents the likelihood that a standard normal variable will fall between these two z-scores.