A distribution with µ = 55 and s = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10.When the distribution is standardized,what value will be obtained for a score of X = 58 from the original distribution?
A)X = 53
B)X = 55
C)X = 58
D)X = 61

Question

A distribution with µ = 55 and s = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10.When the distribution is standardized,what value will be obtained for a score of X = 58 from the original distribution?​
A)​X = 53
B)​X = 55
C)​X = 58
D)​X = 61

Quizplus · Accepted Answer

We can use the formula for z-scores to standardize the distribution:

z = (X - µ) / s

For the original distribution, X = 58, µ = 55, and s = 6. Plugging in these values, we get:

z = (58 - 55) / 6 = 0.5

Now we need to use the new mean and standard deviation to find the corresponding X value. We can rearrange the z-score formula to solve for X:

X = z * s + µ

For the standardized distribution, z = 0.5, s = 10, and µ = 50. Plugging in these values, we get:

X = 0.5 * 10 + 50 = 55

Therefore, the value obtained for a score of X = 58 from the original distribution is equivalent to a score of X = 55 in the standardized distribution. The best choice is B, as it matches this result.

A Distribution with µ = 55 and S = 6