Question

If z is a standard normal variable, find the probability ____________.

A) P(z > 1)
B) P(z < -1)
C) P(z = 0)
D) P(z between -1 and 1)

Answer 1

The probability can be found by calculating the area under the standard normal curve using the z-score and z-table.

Step-by-step explanation:

The probability can be found by calculating the area under the standard normal curve. To find the probability, you need to calculate the z-score and use the z-table to find the corresponding area.

A) P(z > 1) - The z-score for 1 is 0.8413. Therefore, the probability is 1 - 0.8413 = 0.1587.

B) P(z < -1) - The z-score for -1 is 0.1587. Therefore, the probability is 0.1587.

C) P(z = 0) - The probability of a single point on a continuous distribution like the standard normal curve is always 0. Therefore, the probability is 0.

D) P(z between -1 and 1) - The z-score for -1 is 0.1587 and the z-score for 1 is 0.8413. Therefore, the probability is 0.8413 - 0.1587 = 0.6826.