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 $x$ values for $z = 3.3$ and $z=- 3.3$.
First, solve for $x$ from the formula: $x=\mu+z\sigma$.

Step2: Calculate the lower - bound

For $z=-3.3$, $\mu = 690$, and $\sigma = 14$, we have $x_1=690+(-3.3)\times14=690 - 46.2 = 643.8$.

Step3: Calculate the upper - bound

For $z = 3.3$, $\mu = 690$, and $\sigma = 14$, we have $x_2=690+3.3\times14=690 + 46.2=736.2$.

Step4: Check the options

We check which of the given credit scores lies within the range $643.8

• Option A: $634<643.8$, so it is not within the range.
• Option B: $640<643.8$, so it is not within the range.
• Option C: $643.8<720<736.2$, so it is within the range.
• Option D: $750>736.2$, so it is not within the range.

Answer:

C. 720