A distribution with µ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 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

Quizplus · Accepted Answer

To standardize a score from an original distribution to a new distribution, you can use the formula: $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the score in the original distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation. In this case, we are given the standardized score (45 in the new distribution with $\mu = 50$ and $\sigma = 10$), and we need to find the original score in the distribution with $\mu = 35$ and $\sigma = 8$.First, find the Z-score in the new distribution: $Z = \frac{(45 - 50)}{10} = -0.5$.Then, apply this Z-score to the original distribution to find the original score: $X = Z\sigma + \mu = -0.5 \times 8 + 35 = 31$.Therefore, the original score was 31.

A Distribution with µ = 35 and σ = 8