Question
Which of the following does NOT describe the standard normal distribution? Choose the correct answer below. A. It is a normal distribution with a mean of 0 and a standard deviation of 1 . B. The graph is symmetric. C. The graph is uniform. D. The total area under the curve must equal 1 .
Ask by Lewis Lane. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
C. The graph is uniform.
Solution
To determine which option does NOT describe the standard normal distribution, let's analyze each statement:
A. **It is a normal distribution with a mean of 0 and a standard deviation of 1.**
- This statement is true. The standard normal distribution is defined this way.
B. **The graph is symmetric.**
- This statement is also true. The graph of a normal distribution, including the standard normal distribution, is symmetric about the mean.
C. **The graph is uniform.**
- This statement is false. A uniform distribution has constant probability across its range, while a normal distribution has a bell-shaped curve, which is not uniform.
D. **The total area under the curve must equal 1.**
- This statement is true. For any probability distribution, including the standard normal distribution, the total area under the curve is equal to 1.
Based on this analysis, the correct answer is:
**C. The graph is uniform.**
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
The correct answer is C. The graph is uniform. The standard normal distribution, like any normal distribution, is characterized by a bell-shaped curve, not a uniform shape. In a uniform distribution, every value has the same probability, while in a normal distribution, probabilities vary, peaking at the mean. Understanding this, you can see why option C stands out! It's important to remember that normal distributions have a significant number of data points clustering around the mean, leading to that iconic bell shape.
