Question

find the z - scores for which 88% 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 88% of the area lies between -z and z, the total area in the two tails is \(1 - 0.88=0.12\). The area in each tail is \(\frac{0.12}{2}=0.06\).

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 \(1 - 0.06 = 0.94\). Looking up 0.94 in the standard - normal table (z - table), the z - score corresponding to an area of 0.94 is approximately 1.56. Since the normal distribution is symmetric, the z - scores are \(-1.56,1.56\).

Answer:

-1.56, 1.56