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.
[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.
