Normal Area Right 0A229C

1. **State the problem:** We need to find the area under the standard normal distribution curve to the right of the z-score $0.58$. 2. **Recall the standard normal distribution properties:** The total area under the curve is $1$. The area to the left of a z-score $z$ is given by the cumulative distribution function (CDF), denoted as $\Phi(z)$. 3. **Formula:** The area to the right of $z$ is $$P(z > 0.58) = 1 - \Phi(0.58)$$ 4. **Find $\Phi(0.58)$:** Using standard normal distribution tables or a calculator, $$\Phi(0.58) \approx 0.7190$$ 5. **Calculate the area to the right:** $$P(z > 0.58) = 1 - 0.7190 = 0.2810$$ 6. **Round the answer:** Rounded to three decimal places, $$P(z > 0.58) \approx 0.281$$ **Final answer:** The area to the right of $z=0.58$ under the standard normal curve is approximately $0.281$.