1. **Problem statement:** Find the area under the standard normal distribution curve between $z=0$ and $z=1.5$. 2. **Formula and rules:** The standard normal distribution has mean $0$ and standard deviation $1$. The area between two $z$-scores corresponds to the probability that a standard normal variable falls between those values. 3. **Using the standard normal table or cumulative distribution function (CDF):** - The CDF at $z=0$ is $\Phi(0) = 0.5$ because the distribution is symmetric. - The CDF at $z=1.5$ is approximately $\Phi(1.5) = 0.9332$. 4. **Calculate the area between $z=0$ and $z=1.5$:** $$\text{Area} = \Phi(1.5) - \Phi(0) = 0.9332 - 0.5 = 0.4332$$ 5. **Interpretation:** This means about 43.32% of the data under the standard normal curve lies between $z=0$ and $z=1.5$. **Final answer:** $$\boxed{0.4332}$$