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​ Tuesday's ​z-score. Was Tuesday a significantly good​ day?

Answer 1

Answer:

Tuesday z-score was 3.26.

Tuesday was a significantly good day.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A score is said to be significantly high if it has a z-score higher than 1.64, that is, it is at least in the 95th percentile.

In this problem, we have that:

$\mu = 28372.72, \sigma = 2000$

On​ Tuesday, the store sold​ $34,885.21 worth of goods. Find​ Tuesday's ​z-score.

This is Z when $X = 34885.21$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34885.21 - 28372.72}{2000}$

$Z = 3.26$

Tuesday z-score was 3.26.

Was Tuesday a significantly good​ day?

A z-score of 3.26 has a pvalue of 0.9994. So only 1-0.9994 = 0.0006 = 0.06% of the day are better than Tuesday.

So yes, Tuesday was a significantly good day.