Question

a department store has daily mean sales of $28,372.72. the standard deviation of sales is $2000. on tuesday, the store sold $34,885.21 worth of goods. find tuesdays z - score. was tuesday a significantly good day?

a. 3.42, no
b. 3.57, yes
c. 3.26, yes
d. 2.61, no

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We have $\mu = 28372.72$, $\sigma=2000$, and $x = 34885.21$.

Step3: Calculate z - score

$z=\frac{34885.21 - 28372.72}{2000}=\frac{6512.49}{2000}=3.256245\approx3.26$.
A z - score of 3.26 indicates that Tuesday's sales are significantly above the mean (usually, a z - score greater than 2 or 3 is considered significant).

Answer:

C. 3.26, yes