1. The problem asks to find the area under the standard normal distribution curve to the left of $z = 2.25$. 2. The standard normal distribution has a mean of 0 and standard deviation of 1. The area to the left corresponds to the cumulative distribution function (CDF) value at $z=2.25$. 3. Using standard normal distribution tables or a calculator, find $P(Z < 2.25)$. 4. From the table, $P(Z < 2.25) = 0.9878$. This means the area under the curve to the left of $z=2.25$ is 0.9878. 5. Therefore, the final answer is \[ \boxed{0.9878} \].