Using z-scores,a population with µ = 37 and s = 6 is standardized so that the new mean is µ = 50 and s = 10.After the standardization,one individual has a score of X = 55.What was this individual's score in the original distribution?
A)X = 40
B)X = 42
C)X = 43
D)It cannot be determined with the information given.

Question

Using z-scores,a population with µ = 37 and s = 6 is standardized so that the new mean is µ = 50 and s = 10.After the standardization,one individual has a score of X = 55.What was this individual's score in the original distribution?​
A)​X = 40
B)​X = 42
C)​X = 43
D)​It cannot be determined with the information given.

Quizplus · Accepted Answer

The individual's z-score in the standardized distribution can be calculated using the formula $z = \frac{X - \mu}{s}$, where $X$ is the individual's score in the standardized distribution, $\mu$ is the mean of the standardized distribution, and $s$ is the standard deviation of the standardized distribution. Plugging in the given values, $z = \frac{55 - 50}{10} = 0.5$. To find the individual's original score, we use the z-score formula with the original distribution's parameters: $X = \mu + z \times s$, where $\mu = 37$ and $s = 6$. Thus, $X = 37 + 0.5 \times 6 = 40$.

Using Z-Scores,a Population with µ = 37 and S =