Question

find the z - scores for which 75% of the distributions area lies between -z and z. click to view page 1 of the table. click to view page 2 of the table. the z - scores are. (use a comma to separate answers as needed. round to two decimal places as needed.)

Explanation:

Step1: Determine the area in the tails

Since 75% of the area lies between -z and z, the total area in the two tails is 1 - 0.75=0.25. The area in each tail is $\frac{0.25}{2}=0.125$.

Step2: Find the z - score using the standard normal table

We want to find the z - score such that the area to the left of it is 1 - 0.125 = 0.875. Looking up 0.875 in the standard - normal table (z - table), the corresponding z - score is approximately 1.15. Since the standard normal distribution is symmetric, the z - scores are - 1.15 and 1.15.

Answer:

-1.15, 1.15