Question

Consider the random variable X sim N(5, 4²)

Select the value of SD(X)
a.16
b.none of these
c.4
d.5
e.2.2

Answer 1

The standard deviation (SD) of a random variable X that follows a normal distribution N(5, 4²) is 4. This is because the standard deviation is the square root of the variance, which is provided as 16 (the square of 4).

Step-by-step explanation:

The random variable X is normally distributed with a mean (μ) of 5 and a variance (σ²) of 16. The standard deviation (SD) of X is the square root of the variance, which is 4. Therefore, the correct answer is c. 4. When working with normal distributions, the standard deviation is critical for understanding the spread of data around the mean.

In general, for a normal distribution denoted by X ~ N(μ, σ²), the parameter 'μ' represents the mean of the distribution, and 'σ²' represents the variance. The standard deviation is represented by 'σ' and is equal to the square root of the variance.