Question

1. a department store, on average, has daily 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 an unusually good day? a) 3.26, yes b) 3.42, no c) 2.61, no d) 3.57, yes find the number of standard deviations from the mean.

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 are given that $\mu = 28372.72$, $\sigma=2000$, and $x = 34885.21$.

Step3: Calculate z - score

$z=\frac{34885.21 - 28372.72}{2000}=\frac{6512.49}{2000}=3.256245\approx3.26$.

Step4: Determine if it's an unusual day

A z - score with an absolute value greater than 2 (by the range - rule - of - thumb for significant z - scores) indicates an unusual value. Since $z = 3.26>2$, Tuesday was an unusually good day.

Answer:

A. 3.26, yes