If the standard normal deviate of a random variable value of x = 2 is z = -2, while the standard deviation of the random variable x equals 2, then the mean of x is:

A) 6
B) 4
C) 8
D) 2
E) 0

Question

If the standard normal deviate of a random variable value of x = 2 is z = -2, while the standard deviation of the random variable x equals 2, then the mean of x is:A)  6B)  4C)  8D)  2E)  0

Raphael Perot · Accepted Answer

Final Answer : A, Explanation :   The standard normal deviate (z-score) is calculated as   z = x − μ σ z = \frac{x - \mu}{\sigma} z = σ x − μ ​  , where   x x x   is the value of the random variable,   μ \mu μ   is the mean, and   σ \sigma σ   is the standard deviation. Given   z = − 2 z = -2 z = − 2  ,   x = 2 x = 2 x = 2  , and   σ = 2 \sigma = 2 σ = 2  , we can solve for   μ \mu μ  :   − 2 = 2 − μ 2 -2 = \frac{2 - \mu}{2} − 2 = 2 2 − μ ​  . Solving for   μ \mu μ   gives   μ = 6 \mu = 6 μ = 6  .

If the standard normal deviate of a random variable value of x = 2 is z = -2, while the standard deviation of the random variable x equals 2, then the mean of x is:

A) 6
B) 4
C) 8
D) 2
E) 0

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