Use a calculator to find the z–scores of the region shown in the standard normal distribution below.
A = 0.800

• A. $z=-0.26,z=0.26$
• B. $z=-0.25,z=0.25$
• C. $z=-0.805,z=0.805$
• D. $z=-1.28,z=1.28$

Answer: (D)

Verified step by step guidance

1. Begin by understanding that the problem involves finding the z-scores that correspond to a central area of 0.800 under the standard normal distribution curve.
2. Sketch a standard normal distribution curve, which is symmetric around the mean (0). The area under the curve represents probabilities, and the total area is 1.
3. Identify that the shaded area in the graph is 0.800, which is the probability between the two z-scores, -z and z. This means that the tails on either side of the shaded area have a combined probability of 0.200.
4. Divide the tail area by 2 to find the probability in each tail: 0.200 / 2 = 0.100. This is the area in each tail beyond the z-scores.
5. Use a standard normal distribution table or calculator to find the z-score that corresponds to a cumulative probability of 0.100 in the left tail. This z-score will be negative, and its positive counterpart will be the z-score for the right tail. The correct z-scores are approximately -1.28 and 1.28.