Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 28372.72, \sigma = 2000[/tex]
On Tuesday, the store sold $34,885.21 worth of goods. Find Tuesday's z-score.
This is Z when [tex]X = 34885.21[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{34885.21 - 28372.72}{2000}[/tex]
[tex]Z = 3.26[/tex]
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.
