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
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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](https://tex.z-dn.net/?f=%5Cmu%20%3D%2028372.72%2C%20%5Csigma%20%3D%202000)
On Tuesday, the store sold $34,885.21 worth of goods. Find Tuesday's z-score.
This is Z when ![X = 34885.21](https://tex.z-dn.net/?f=X%20%3D%2034885.21)
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{34885.21 - 28372.72}{2000}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B34885.21%20-%2028372.72%7D%7B2000%7D)
![Z = 3.26](https://tex.z-dn.net/?f=Z%20%3D%203.26)
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.