The notation za is the z-score such that the area under the standard normal curve to the right of za is _______.

Verified step by step guidance

1. Understand that the notation \(z_\alpha\) represents a specific z-score on the standard normal distribution.
2. Recall that the standard normal distribution is symmetric and has a total area of 1 under its curve.
3. The area to the right of \(z_\alpha\) corresponds to the probability that a standard normal variable is greater than \(z_\alpha\).
4. By definition, \(z_\alpha\) is the z-score such that the area to the right of it under the standard normal curve is exactly \(\alpha\).
5. Therefore, \(z_\alpha\) satisfies the condition: \(P(Z > z_\alpha) = \alpha\), where \(Z\) is a standard normal random variable.

Key Concepts

Z-Score

A z-score represents the number of standard deviations a data point is from the mean in a standard normal distribution. It standardizes values, allowing comparison across different normal distributions.

Standard Normal Distribution

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is symmetric and used as a reference to find probabilities and z-scores.

Area Under the Curve (Tail Probability)

The area under the standard normal curve to the right of a z-score represents the probability that a value is greater than that z-score. This tail area is used to find critical values in hypothesis testing.