Final answer:
Approximately 3.06% of the population lies to the left of the z-score -1.87 in a normal distribution, as indicated by the z-table for this z-score.
Step-by-step explanation:
The question asks about the percentage of a population that lies to the left of the z-score -1.87 in a normal distribution. In a normal distribution, a z-score quantifies the number of standard deviations a data point is from the mean. Negative z-scores indicate values below the mean.
To find the percentage of the population that lies to the left of a given z-score, one can refer to a standard normal distribution table, also known as a z-table. For a z-score of -1.87, the z-table indicates that approximately 3.06% of the population lies to the left side. This reflects the area under the curve to the left of the z-score on the normal distribution graph.
This understanding is based on the empirical rule or 68-95-99.7 rule, which states that about 68 percent of the values lie within one standard deviation of the mean (z-scores -1 to +1), about 95 percent within two (z-scores -2 to +2), and about 99.7 percent within three (z-scores -3 to +3).