Q: For which of the following random variables would the use of a Normal distribution as a model be a clear error?
or
Q: Using a normal distribution as a model would be obviously incorrect for which of the following random variables?
- The number of houses that an individual owns
- The number of minutes that a battery lasts in a cell phone
- Student test scores on an exam
- The daily percentage change on a stock
Explanation: Normal distribution is characterized by its continuity and the ability to take on any real number, including negative values. However, the number of houses an individual owns is a discrete random variable that can only take on non-negative integer values (0, 1, 2, …). It cannot be negative and has a limited range, making it unsuitable for modeling with a Normal distribution, which is continuous and can have values across the entire real number line.
