A population has a mean $\mu = 55$ and standard deviation $\sigma = 9$ What number has a z -score of -0.5 ?
A) -59.5
B) 50.5
C) -6.2
D) -4.5

Question

A population has a mean $\mu = 55$ and standard deviation $\sigma = 9$ What number has a  z -score of  -0.5 ? 
A)  -59.5 
B)  50.5 
C)  -6.2 
D)  -4.5

Quizplus · Accepted Answer

The formula for calculating a z-score is $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given z-score of -0.5, the mean of 55, and the standard deviation of 9, we solve for $X$: $-0.5 = \frac{(X - 55)}{9}$. Solving for $X$ gives $X = 55 + (-0.5)(9) = 55 - 4.5 = 50.5$.

A Population Has a Mean μ=55\mu = 55μ=55 And Standard Deviation σ=9\sigma = 9σ=9

A Population Has a Mean $\mu = 55$ And Standard Deviation $\sigma = 9$