Question

In Standard normal distribution, the value of median is _______

• A. 1.0
• B. Any positive number
• C. 5.0
• D. 0.0

Hint:

For any normal distribution $N(\mu, \sigma^2)$, the mean, median, and mode are always equal to the parameter $\mu$. For a standard normal distribution, $\mu = 0$, so the median is $0$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The standard normal distribution is a continuous probability distribution characterized by its symmetrical bell shape.

Step 2: Detailed Explanation:
The standard normal distribution (often denoted by $Z$) is defined with a mean ($\mu$) of 0 and a standard deviation ($\sigma$) of 1: \[ Z \sim N(0, 1) \]
One of the defining properties of any symmetric, unimodal distribution is that its measures of central tendency coincide at the center of symmetry.
For the standard normal curve, this center of symmetry lies at the point $Z = 0$.
As a result: \[ \text{Mean} = \text{Median} = \text{Mode} = 0 \]
The median divides the area under the standard normal curve into two equal halves of 0.5 each.
Thus, the value of the median is exactly 0.0.

Step 3: Final Answer:
The value of the median is 0.0.