Question
Find the area under the standard normal distribution curve between \( z=0 \) and \( z=0 \). Use 0 The Standard Normal Distribution Table. Round your answer to at least 4 decimal places.
Ask by Moran Hodges. in the United States
Mar 22,2025
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Tutor-Verified Answer
Answer
The area under the standard normal curve between \( z=0 \) and \( z=0 \) is 0.0000.
Solution
The area under the standard normal curve between \( z=0 \) and \( z=0 \) is computed by finding the difference between the cumulative probabilities at the two endpoints.
1. For \( z=0 \), the cumulative distribution function is:
\[
\Phi(0)=0.5
\]
2. The area between \( z=0 \) and \( z=0 \) is:
\[
\Phi(0)-\Phi(0)=0.5-0.5=0
\]
Rounded to four decimal places, the area is:
\[
0.0000
\]
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Simplify this solution Beyond the Answer
Interestingly, the area under the standard normal distribution curve between \( z=0 \) and \( z=0 \) is exactly zero. Why? Because you’re essentially looking at a line segment with no width, which means there's no area to capture! In real-world applications, the standard normal distribution is often used to determine probabilities and assess how data falls around the mean. Areas under the curve help us understand the likelihood of different outcomes. For example, if you were analyzing test scores, you can find the likelihood that a randomly chosen score falls within a certain range.
