Final answer:
The probability that the standard normal variable lies below -3 is found using the standard normal distribution table. The area to the left of the z-score -3 is 0.0013, which corresponds to option D in your multiple choice question.
Step-by-step explanation:
You are asking about the probability that the value of the standard normal variable lies below -3. To find this probability, we utilize the standard normal distribution table which provides the area under the normal curve to the left of a given z-score (the number of standard deviations from the mean). The z-score in this case is -3.
According to the standard normal distribution table, the area to the left of -3 is very small. This area represents the probability that a standard normal variable is less than -3. Most standard normal tables do not provide values for z-scores smaller than -3 because the areas are so small. However, the typical value given for a z-score of -3 is 0.0013, which corresponds to option D.