Final Answer:
The probability that a data point in the set takes on a value less than X is extremely low, approaching zero.
Step-by-step explanation:
The z-score is a measure of how many standard deviations a data point is from the mean in a normal distribution. A z-score of -4.5 indicates an extremely rare event, as it means the data point is 4.5 standard deviations below the mean. In a standard normal distribution, about 99.7% of the data falls within 3 standard deviations of the mean. Therefore, a z-score of -4.5 is well beyond this range, suggesting an almost negligible probability.
To understand this intuitively, imagine a bell curve representing the normal distribution. A z-score of -4.5 places the data point far in the tail of the curve. The probability of finding a data point even further to the left (less than X) is minuscule.
In practical terms, this implies that the likelihood of encountering a data point with a value less than X is close to zero in a normally distributed data set. Extreme z-scores represent outliers, and their occurrence is highly improbable in the context of a standard normal distribution.