If  X is normally distributed with mean -2 and variance 25 then the standard normal variate isans.

The standard normal variate (Z) of a normally distributed random variable (X) is given by the formula:

Z = (X - μ) / σ

where:

• X is the random variable,
• μ is the mean of the distribution, and
• σ is the standard deviation of the distribution.

In this case, X is normally distributed with a mean (μ) of -2 and a variance of 25. The standard deviation (σ) is the square root of the variance, so σ = √25 = 5.

Substituting these values into the formula gives:

Z = (X - (-2)) / 5 or Z = (X + 2) / 5

So, the standard normal variate of X is (X + 2) / 5.