Which of the following best describes the shaded region on a standard normal distribution curve that corresponds to the probability $P(a<z<b)$?

• A. The area under the curve to the left of $z=a$ is shaded.
• B. The area under the curve to the right of $z=b$ is shaded.
• C. The area under the curve between $z=a$ and $z=b$ is shaded.
• D. The entire area under the curve is shaded.

Answer: (C)

Verified step by step guidance

1. Understand that the standard normal distribution curve is symmetric and represents probabilities as areas under the curve.
2. Recognize that the notation \(P(a < z < b)\) refers to the probability that the random variable \(z\) falls between two values \(a\) and \(b\).
3. Recall that probabilities in a continuous distribution correspond to the area under the curve between the specified values.
4. Identify that \(P(a < z < b)\) means the shaded region is the area under the curve starting at \(z = a\) and ending at \(z = b\).
5. Conclude that the correct description of the shaded region is the area under the curve between \(z = a\) and \(z = b\).