1. **Problem:** Find the area under the standard normal curve for z between 1.03 and 2.79. 2. **Formula:** The area between two z-values $z_1$ and $z_2$ is given by $P(z_1 < Z < z_2) = \Phi(z_2) - \Phi(z_1)$ where $\Phi(z)$ is the cumulative distribution function (CDF) of the standard normal distribution. 3. **Step-by-step solution:** 1. Find $\Phi(2.79)$ and $\Phi(1.03)$ from standard normal tables or a calculator. 2. Using a standard normal table or calculator: - $\Phi(2.79) \approx 0.9973$ - $\Phi(1.03) \approx 0.8485$ 3. Calculate the area: $$P(1.03 < Z < 2.79) = 0.9973 - 0.8485 = 0.1488$$ 4. **Interpretation:** The probability that a standard normal variable falls between 1.03 and 2.79 is approximately 0.1488 or 14.88%.