A distribution with µ = 35 and s = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10.In the new,standardized distribution your score is X = 45.What was your score in the original distribution?
A)X = 30
B)X = 31
C)X = 39
D)X = 45

Question

A distribution with µ = 35 and s = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10.In the new,standardized distribution your score is X = 45.What was your score in the original distribution?​
A)​X = 30
B)​X = 31
C)​X = 39
D)​X = 45

Quizplus · Accepted Answer

To find the original score $X$ in the original distribution from the standardized score, we use the formula for standardization: $Z = \frac{X - \mu}{s}$, where $Z$ is the standardized score, $X$ is the original score, $\mu$ is the mean, and $s$ is the standard deviation. However, since we are reversing the process, we rearrange the formula to solve for $X$: $X = Zs + \mu$. Given that in the new distribution, $\mu = 50$, $s = 10$, and $X = 45$, we first find the standardized score $Z$ in the new distribution: $Z = \frac{45 - 50}{10} = -0.5$. Then, we apply this $Z$ to the original distribution to find the original score: $X = -0.5(8) + 35 = -4 + 35 = 31$.

A Distribution with µ = 35 and S = 8