For a sample with [tex]M=50[/tex] and [tex]s=12[/tex], what is the [tex]X[/tex] value corresponding to [tex]z=-0.25[/tex]?

A. 47
B. 53
C. 46
D. 54



Answer :

To find the value of [tex]\(X\)[/tex] corresponding to a given [tex]\(z\)[/tex]-score, we can use the formula for calculating the [tex]\(X\)[/tex] value from a [tex]\(z\)[/tex]-score, the mean ([tex]\(M\)[/tex]), and the standard deviation ([tex]\(s\)[/tex]):

[tex]\[ X = M + z \cdot s \][/tex]

Here are the given values:
- The mean ([tex]\(M\)[/tex]) is 50.
- The standard deviation ([tex]\(s\)[/tex]) is 12.
- The [tex]\(z\)[/tex]-score ([tex]\(z\)[/tex]) is -0.25.

Following the formula step-by-step:

1. Multiply the [tex]\(z\)[/tex]-score by the standard deviation:
[tex]\[ z \cdot s = -0.25 \cdot 12 = -3 \][/tex]

2. Add this result to the mean:
[tex]\[ X = M + (-3) = 50 - 3 = 47 \][/tex]

Therefore, the [tex]\(X\)[/tex] value corresponding to the [tex]\(z\)[/tex]-score of -0.25 is [tex]\( \boxed{47} \)[/tex]. This matches option A, so the correct answer is A. 47.