Question

1. the mean amount of money withdrawn from a bank atm on a certain day was $120. if lauren withdrew $80 and her z-score was -3.2, what was the standard deviation for the amount withdrawn that day?

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $z$ is the z - score, $x$ is the individual value, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $z=- 3.2$, $x = 80$, and $\mu=120$. We need to solve for $\sigma$.

Step2: Substitute values into the formula

Substitute the known values into the z - score formula: $-3.2=\frac{80 - 120}{\sigma}$.

Step3: Simplify the numerator

Simplify the numerator: $80 - 120=-40$. So the equation becomes $-3.2=\frac{-40}{\sigma}$.

Step4: Solve for $\sigma$

Multiply both sides of the equation by $\sigma$: $-3.2\sigma=-40$. Then divide both sides by $- 3.2$: $\sigma=\frac{-40}{-3.2}=12.5$.

Answer:

12.5