If the z-value for a given value x of the random variable X is z = 2.326, and the distribution of X is normal with a mean of 50 and a standard deviation of 5, to what x-value does this z-value correspond?
A) 11.63 .
B) 61.63 .
C) 63.16 .
D) 16.31 .

Question

If the z-value for a given value x of the random variable X is z = 2.326, and the distribution of X is normal with a mean of 50 and a standard deviation of 5, to what x-value does this z-value correspond? 
A)  11.63 . 
B) 61.63 . 
C)  63.16 . 
D)  16.31 .

Quizplus · Accepted Answer

We can use the formula for standardizing a normal distribution: 
z = (x - mu) / sigma 
where mu = mean, sigma = standard deviation. 
Rearranging the formula to solve for x: 
x = z * sigma + mu 
Substituting in the given values: 
x = 2.326 * 5 + 50 = 61.63 
Therefore, the z-value of 2.326 corresponds to the x-value of 61.63.

If the Z-Value for a Given Value X of the Random