Question

Find the z-score that has 20.9% of the distribution's area to its left.

a) -0.85
b) -0.91
c) -0.79
d) -0.96

Answer 1

The z-score with 20.9% of the distribution's area to its left is -0.79. This is determined by using a Z-table to find the z-score closest to the area percentage required.

Step-by-step explanation:

The student is tasked with finding the z-score that corresponds to having 20.9% of the area of the standard normal distribution to its left. To do this, we refer to a Z-table, which provides the area to the left of certain z-scores. The objective is to find the z-score closest to an area of 0.209 (or 20.9%).

Looking at the options provided, we check each z-score against the Z-table:

• -0.85 has an area to the left of approximately 0.1977.
• -0.91 has an area to the left of approximately 0.1814.
• -0.79 has an area to the left of approximately 0.2148.
• -0.96 has an area to the left of approximately 0.1685.

The z-score of -0.79 is the closest to providing an area to the left of 0.209, making it the correct answer.