In a standard normal probability distribution, the area to the left portion of the mean is equal to? -0.5 0.5 any value between 0 and 1 1

Breakdown the Problem

1. Identify the characteristics of a standard normal distribution.
2. Determine the significance of the mean in this context.

Relevant Concepts

1. A standard normal distribution is a symmetric probability distribution.
2. The mean (μ) of the standard normal distribution is 0.
3. The area under the curve represents probability.

Analysis and Detail

1. In a standard normal distribution, the total area under the curve is 1.
2. Because the distribution is symmetric around the mean, the area to the left of the mean (0) is equal to the area to the right of the mean.
3. Therefore, the area to the left of the mean is: $\text{Area to the left of mean} = \frac{1}{2} = 0.5$

Verify and Summarize

Since the total area under the curve is 1, and it is symmetric, each half (to the left and right of the mean) must represent an area of 0.5.

Final Answer

The area to the left portion of the mean is 0.5.