Question

the mean of a set of credit scores is $mu = 690$ and $sigma = 14$. which credit score is within a z - score of 3.3?
634
640
720
750

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to find the range of values within $z = 3.3$. Rearranging the formula for $x$ gives $x=\mu\pm z\sigma$.

Step2: Calculate the lower bound

$x_{lower}=\mu - z\sigma$. Substitute $\mu = 690$, $z = 3.3$, and $\sigma = 14$ into the formula: $x_{lower}=690-3.3\times14=690 - 46.2 = 643.8$.

Step3: Calculate the upper bound

$x_{upper}=\mu + z\sigma$. Substitute $\mu = 690$, $z = 3.3$, and $\sigma = 14$ into the formula: $x_{upper}=690 + 3.3\times14=690+46.2 = 736.2$.

Step4: Check the options

A. 634 is less than 643.8.
B. 640 is less than 643.8.
C. 720 is between 643.8 and 736.2.
D. 750 is greater than 736.2.
So the credit score within a z - score of 3.3 is 720.

Answer:

C. 720