Final answer:
To find the z-score where the area to its left is 0.09, look up the area closest to 0.91 in the z-table and find the corresponding z-score, which is 1.34. Then take the negative of this value, yielding a z-score of -1.34.
Step-by-step explanation:
The student is asking how to find the z-score for which the area to its left is 0.09 using the Cumulative Normal Distribution Table. The process to find this z-score involves searching the table for the closest area to 0.09 and then noting the corresponding z-score. However, since typical z-tables provide values for areas to the left starting from the center (0.5 and above), you may need to use the symmetry of the normal distribution curve to look up the area equal to 1 - 0.09 which is 0.91. After finding the corresponding positive z-score for 0.91, you would take its negative to find the z-score for an area of 0.09 to the left.
The z-table indicates that the area closest to 0.91 corresponds to a z-score of 1.34. Therefore, the z-score we are looking for is -1.34, as the negative of this value indicates that the left tail encompasses 0.09 of the area under the curve.