Find the area, to the nearest thousandth, of the indicated region of the standard normal distribution. The region where $z<-0.75$ square unit

Step 1 ：The problem is asking for the area under the curve of the standard normal distribution where \(z < -0.75\).

Step 2 ：The standard normal distribution is a probability distribution with a mean of 0 and a standard deviation of 1. The area under the curve of this distribution represents the probability of an event occurring.

Step 3 ：To find this, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.

Step 4 ：Let's denote the value of \(z\) as -0.75.

Step 5 ：By using the CDF, we find that the area under the curve for \(z < -0.75\) is approximately 0.227.

Step 6 ：This means that there is a 22.7% probability that a random variable from a standard normal distribution is less than -0.75.

Step 7 ：Final Answer: The area of the region where \(z<-0.75\) is approximately \(\boxed{0.227}\) square units.