To determine which credit scores fall within a z-score of 3.3 from the mean, we need to consider the range of values that lie within this interval.
Given:
- The mean (μ) is 690.
- The standard deviation (σ) is 14.
- The z-score threshold is 3.3.
The range within a z-score of 3.3 can be calculated as follows:
1. Calculate the lower bound of the range:
[tex]\[
\text{Lower bound} = \mu - z \cdot \sigma
\][/tex]
Substituting the given values:
[tex]\[
\text{Lower bound} = 690 - 3.3 \cdot 14 = 643.8
\][/tex]
2. Calculate the upper bound of the range:
[tex]\[
\text{Upper bound} = \mu + z \cdot \sigma
\][/tex]
Substituting the given values:
[tex]\[
\text{Upper bound} = 690 + 3.3 \cdot 14 = 736.2
\][/tex]
The range of credit scores within a z-score of 3.3 is from 643.8 to 736.2. Now, we will check which of the given credit scores lie within this range:
- 634: This is below 643.8, so it is not within the range.
- 640: This is below 643.8, so it is not within the range.
- 720: This is within the range of 643.8 to 736.2.
- 750: This is above 736.2, so it is not within the range.
Therefore, the credit score that is within a z-score of 3.3 from the mean is 720.
