Question

For the standard normal distribution Z ~ N(0, 1), which of the following is true?

i) P(Z < -2.15) = P(Z > 2.15)
ii) P(Z < 1.86) = P(Z > -1.86)
a) Both i and ii are correct
b) Only i is correct
c) Only ii is correct
d) Neither i nor ii is correct

Answer 1

In the standard normal distribution, P(Z < -2.15) is equal to P(Z > 2.15), making statement i) true. However, P(Z < 1.86) is different than P(Z > -1.86), making statement ii) false.

Step-by-step explanation:

To determine which of the given statements are true, we need to consider the properties of the standard normal distribution. In the standard normal distribution, the cumulative probability to the left of a z-score is equal to the cumulative probability to the right of the negative of that z-score. Therefore, for statement i), P(Z < -2.15) is equal to the same as P(Z > 2.15), making the statement true. For statement ii), P(Z < 1.86) is different than P(Z > -1.86), making the statement false. Therefore, the correct answer is b) Only i is correct.

Answer 2

Both statements i and ii are correct.

Step-by-step explanation:

To determine if the statements are true or false, we need to find the probabilities of the given events using the standard normal distribution table.

1. P(Z < -2.15) = 0.0158, P(Z > 2.15) = 0.0158. Therefore, statement i is true.
2. P(Z < 1.86) = 0.9686, P(Z > -1.86) = 0.9686. Therefore, statement ii is true.

Hence, both statement i and ii are correct, so the answer is a) Both i and ii are correct.