MATH SOLVE

9 months ago

Q:
# If x is a normal random variable with a standard deviation of 10, then 3x has a standard deviation equal to:

Accepted Solution

A:

standard deviation(σ[tex]_{x} [/tex]) = √V(X) = 10

Therefore, variance of X. V(X) = 10² = 100

Variance of aX is given by,

V(aX) = a²V(X)

Therefore, variance of 3X will be,

V(3X) = 3²V(X) = 9(100) = 900

Therefore, standard deviation of 3X is,

σ[tex]_{3x} [/tex] = √V(3X) = √900 = 30

Therefore, variance of X. V(X) = 10² = 100

Variance of aX is given by,

V(aX) = a²V(X)

Therefore, variance of 3X will be,

V(3X) = 3²V(X) = 9(100) = 900

Therefore, standard deviation of 3X is,

σ[tex]_{3x} [/tex] = √V(3X) = √900 = 30