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

Z = (X - μ) / σ

where μ is the mean and σ is the standard deviation (which is the square root of the variance).

Given that X is normally distributed with mean -2 and variance 25, the standard deviation σ is the square root of 25, which is 5.

Substituting these values into the formula gives:

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

So, the correct answer is (X + 2) / 5.

Question

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

Z = (X - μ) / σ

where μ is the mean and σ is the standard deviation (which is the square root of the variance).

Given that X is normally distributed with mean -2 and variance 25, the standard deviation σ is the square root of 25, which is 5.

Substituting these values into the formula gives:

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

So, the correct answer is (X + 2) / 5.

Knowee AI · Accepted Answer

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

Z = (X - μ) / σ

where μ is the mean and σ is the standard deviation (which is the square root of the variance).

Given that X is normally distributed with mean -2 and variance 25, the standard deviation σ is the square root of 25, which is 5.

Substituting these values into the formula gives:

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

So, the correct answer is (X + 2) / 5.

If X is normally distributed with mean -2 and variance 25 then the standard normal variate is ans. (X-2)/5 (X+2)/5 (X-25)/2 none of these