Using the standard normal curve, the area between z = 0 and z = 3.50 is about 0.50.Group of answer choicesTrueFalse

Break Down the Problem

1. Identify the total area under the standard normal curve between $z = 0$ and $z = 3.50$.
2. Understand properties of the standard normal distribution, where the mean is 0 and the standard deviation is 1.

Relevant Concepts

1. The area under the standard normal curve represents probabilities.
2. The total area under the curve from $z = -\infty$ to $z = +\infty$ is 1.
3. The area from $z = 0$ to $z = 3.50$ is a portion of this distribution.

Analysis and Detail

1. The area from the mean (z = 0) to any value can be obtained from standard normal distribution tables or a calculator.
2. For $z = 3.50$, the cumulative area from $z = -\infty$ to $z = 3.50$ is approximately 0.99977.
3. To find the area between $z = 0$ and $z = 3.50$: $\text{Area}(0 \text{ to } 3.50) = \Phi(3.50) - \Phi(0)$ where $\Phi(0) = 0.5$. So: $\text{Area}(0 \text{ to } 3.50) \approx 0.99977 - 0.5 = 0.49977 \approx 0.50$

Verify and Summarize

The calculated area between $z = 0$ and $z = 3.50$ is approximately 0.50. This closely matches the value stated in the question.

Final Answer

True. The area between $z = 0$ and $z = 3.50$ is about 0.50.