1. The problem is to find the area under the standard normal curve, which corresponds to the probability for a standard normal random variable. 2. The standard normal curve is the probability density function of a normal distribution with mean $\mu=0$ and standard deviation $\sigma=1$. The total area under this curve is 1. 3. The area under the curve between two points $a$ and $b$ is given by the integral of the standard normal density function $\phi(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$ from $a$ to $b$: $$\text{Area} = \int_a^b \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} dx$$ 4. Since the problem does not specify limits $a$ and $b$, the area under the entire standard normal curve is 1. 5. If you want the area to the left of a value $z$, you use the cumulative distribution function (CDF) $\Phi(z)$, which is tabulated or computed using software. 6. For example, the area to the left of $z=0$ is $\Phi(0) = 0.5$ because the standard normal distribution is symmetric. 7. To find the area between any two points, say $z_1$ and $z_2$, compute $\Phi(z_2) - \Phi(z_1)$. Final answer: The total area under the standard normal curve is 1.