Question

If Z is a random variable from a standard normal distribution and P(Z > c) = 0.39, then P(Z < -c) = 0.39.

a) True
b) False

Answer 1

The statement is False. If P(Z > c) = 0.39, this means that the area to the right of c under the standard normal curve is 0.39. In other words, the area to the left of c is 1 - 0.39 = 0.61. Therefore, P(Z < -c) is not equal to 0.39.

Step-by-step explanation:

The statement is b) False.

If P(Z > c) = 0.39, this means that the area to the right of c under the standard normal curve is 0.39. In other words, the area to the left of c is 1 - 0.39 = 0.61.

Therefore, P(Z < -c) is not equal to 0.39. To find P(Z < -c), we can use the symmetry property of the standard normal distribution. Since -c is the same distance from 0 as c, the area to the left of -c is equal to the area to the right of c. So, P(Z < -c) = 0.61, not 0.39.