For a standard normal distribution, which of the following expressions must always be equal to 1?
OP(zs-a)-P(-asza)-P(zza)
OP(zs-a)-P(-asza)+P(zza)
OP(zs-a)+P(-asza)-Pizza)
OP(zs-a)+P(-aza)+P(za)



Answer :

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.