The expression that must always be equal to 1 for a standard normal distribution is:
\[ P(z \leq a) + P(z \geq a) \]
Here's why:
1. \( P(z \leq a) \) represents the probability that a standard normal random variable \( z \) is less than or equal to \( a \).
2. \( P(z \geq a) \) represents the probability that a standard normal random variable \( z \) is greater than or equal to \( a \).
When you add these two probabilities together, you are essentially calculating the total probability of all outcomes, which should sum up to 1 in a probability distribution.
Therefore, the expression \( P(z \leq a) + P(z \geq a) \) must always be equal to 1 for a standard normal distribution.
