the mean of a set of credit scores is $mu = 690$ and $sigma = 14$. which credit score is within a z - score…

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 $z=- 3.3$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step2: Calculate the lower - bound value of $x$

For $z=-3.3$, $\mu = 690$, and $\sigma = 14$, we substitute into the formula $x=\mu+z\sigma$. So $x_{lower}=690+( - 3.3)\times14=690 - 46.2 = 643.8$.

Step3: Calculate the upper - bound value of $x$

For $z = 3.3$, $\mu = 690$, and $\sigma = 14$, we substitute into the formula $x=\mu+z\sigma$. So $x_{upper}=690 + 3.3\times14=690+46.2 = 736.2$.

Step4: Check the options

We check each option:

• Option 1: $634<643.8$, so it is not within the range.
• Option 2: $640<643.8$, so it is not within the range.
• Option 3: $643.8<720<736.2$, so it is within the range.
• Option 4: $750>736.2$, so it is not within the range.

Answer:

720