Question

find the indicated z - scores shown in the graph. click to view page 1 of the standard normal table. click to view page 2 of the standard normal table. the z - scores are . (use a comma to separate answers as needed. round to two decimal places as needed.)

Explanation:

Step1: Recall standard - normal table property

The standard - normal table gives the cumulative probability $P(Z\leq z)$. The area to the left of $z = 0$ is $0.5$.

Step2: Calculate cumulative probability for positive z - score

The cumulative probability for the positive $z$ - score is $0.5+0.4719 = 0.9719$.

Step3: Look up z - score in the standard - normal table

Looking up the value $0.9719$ in the standard - normal table, we find the $z$ - score. The $z$ - value corresponding to a cumulative probability of $0.9719$ is approximately $z = 1.91$.

Step4: Determine negative z - score

Since the standard - normal distribution is symmetric about $z = 0$, the negative $z$ - score corresponding to the left - hand shaded area is $z=- 1.91$.

Answer:

$-1.91,1.91$