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 two - tails

Since 76% of the area lies between -z and z, the area in the two - tails is $1 - 0.76=0.24$. The area in each tail is $\frac{0.24}{2}=0.12$.

Step2: Find the cumulative area to the left of -z

The cumulative area to the left of -z is 0.12.

Step3: Use the standard normal table

Looking up the value 0.12 in the standard - normal table (z - table), the z - score corresponding to a cumulative area of 0.12 is approximately - 1.17.
Since the standard normal distribution is symmetric, the z - score for the right - hand side (z) is the positive value of the left - hand side z - score. So z = 1.17.

Answer:

-1.17, 1.17