Which statement about the normal distribution is true?

Which statement about the normal distribution is true?

• A. It is symmetric and unimodal
• B. It has a defined mean and standard deviation
• C. It has three peaks
• D. It is defined by the median only

Answer: (B)

The key idea here is that a normal distribution is fully described by two numbers: the mean and the standard deviation. The mean sets where the center of the bell is, and the standard deviation determines how wide or narrow the bell is. Because these two parameters completely specify any normal curve, saying it has a defined mean and standard deviation is the precise, foundational description of the distribution. While the curve is indeed symmetric and has one peak, that qualitative property isn’t enough to identify it uniquely, since many distributions can share symmetry and a single peak. The claim that it’s defined by the median only isn’t correct because, even though the mean and median coincide for a normal distribution, you still need the standard deviation (and the mean) to define its exact shape and spread.

The key idea here is that a normal distribution is fully described by two numbers: the mean and the standard deviation. The mean sets where the center of the bell is, and the standard deviation determines how wide or narrow the bell is. Because these two parameters completely specify any normal curve, saying it has a defined mean and standard deviation is the precise, foundational description of the distribution.

While the curve is indeed symmetric and has one peak, that qualitative property isn’t enough to identify it uniquely, since many distributions can share symmetry and a single peak. The claim that it’s defined by the median only isn’t correct because, even though the mean and median coincide for a normal distribution, you still need the standard deviation (and the mean) to define its exact shape and spread.