To find the credit score that corresponds to a given [tex]\(z\)[/tex]-score, we can use the formula:
[tex]\[ X = \mu + z \cdot \sigma \][/tex]
Where:
- [tex]\(\mu\)[/tex] is the mean of the credit scores.
- [tex]\(\sigma\)[/tex] is the standard deviation.
- [tex]\(z\)[/tex] is the [tex]\(z\)[/tex]-score.
- [tex]\(X\)[/tex] is the credit score we are looking for.
Given values:
- The mean, [tex]\(\mu\)[/tex], is 690.
- The standard deviation, [tex]\(\sigma\)[/tex], is 14.
- The [tex]\(z\)[/tex]-score is 3.3.
Plugging in the values:
[tex]\[ X = 690 + 3.3 \cdot 14 \][/tex]
First, calculate [tex]\(3.3 \cdot 14\)[/tex]:
[tex]\[ 3.3 \cdot 14 = 46.2 \][/tex]
Then add this value to the mean:
[tex]\[ X = 690 + 46.2 = 736.2 \][/tex]
Therefore, the credit score that corresponds to a [tex]\(z\)[/tex]-score of 3.3 is 736.2. Let's check the given options:
- 634
- 640
- 720
- 750
None of these options match our calculated value of 736.2 as precise as it should be. Hence, based on the given choices, none of them correspond exactly to a [tex]\(z\)[/tex]-score of 3.3 under the given conditions.
