If a random variable X is normally distributed with mean μ and standard deviation σ, we use the notation: X~N(μ,σ).

Question

For example, X~N(2,1) means that X is normally distributed with mean 2 and standard deviation 1.

Use the above notation to indicate that:

a) random variable X is normally distributed with mean 3 and standard deviation 4

b) random variable X is normally distributed with mean 0 and standard deviation 5

Answer 1

a) The notation for the random variable \( X \) being normally distributed with mean 3 and standard deviation 4 is:
\[ X \sim N(3, 4) \]

b) The notation for the random variable \( X \) being normally distributed with mean 0 and standard deviation 5 is:
\[ X \sim N(0, 5) \]