Question

find the z - scores for which 76% 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 distribution's area lies between -z and z, the total area in the two - tails is \(1 - 0.75=0.25\). So 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 (z - score) table, we find that the z - score corresponding to an area of 0.875 is approximately \(z = 1.15\). Since the normal distribution is symmetric, the z - scores are \(-1.15,1.15\).

Answer:

\(-1.15,1.15\)