What are the values of z that correspond to the P(-z $\le$ Z $\le$ z) equal to 0.4778?
A)±0.2389.
B)± 0.71.
C)±0.64.
D)None of these choices are correct.

Question

What are the values of z that correspond to the P(-z $\le$ Z $\le$  z) equal to 0.4778?
A)±0.2389.
B)± 0.71.
C)±0.64.
D)None of these choices are correct.

Quizplus · Accepted Answer

Using the standard normal distribution table, we can find the z-scores that correspond to a cumulative probability of 0.4778. This probability is associated with the area between -z and z under the standard normal distribution curve. In other words:

P(-z ≤ Z ≤ z) = 0.4778

Since the standard normal distribution is symmetrical around 0, we know that:

P(Z ≥ z) = (1 - 0.4778)/2 = 0.2611

Using the standard normal distribution table again, we can find the z-score that corresponds to a cumulative probability of 0.2611, which is approximately 0.64. Therefore, the values of z that correspond to P(-z ≤ Z ≤ z) equal to 0.4778 are ±0.64.

What Are the Values of Z That Correspond to the P(-Z