Final answer:
The distance corresponding to a z-score of 1.4, derived from the difference in areas from the z-table between a z-score of 1.5 and -0.40, is 0.5886. This value represents the proportion of the area under the normal curve to the left of the given z-score.
Step-by-step explanation:
The z-score of 1.4 corresponds to an area under the normal curve to the left of 1.4. To find the distance corresponding to this z-score, we need to use the z-table. From the given information, we know that the area to the left of a z-score of 1.5 is 0.9332, and the area to the left of a z-score of -0.40 is 0.3446. The difference between these two areas is 0.5886. Therefore, the distance that would have a z-score of 1.4 is 0.5886.