Respuesta :
Answer:
Tuesday's z-score was of -1.325.
The percentile rank of sales for this day was the 9.25th percentile.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600.
This means that [tex]\mu = 21000, \sigma = 3600[/tex]
On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score.
This is Z when X = 16230. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16230 - 21000}{3600}[/tex]
[tex]Z = -1.325[/tex]
Tuesday's z-score was of -1.325.
What is the percentile rank of sales for this day
This is the p-value of Z = -1.325.
Looking at the z-table, this is of 0.0925, and thus:
The percentile rank of sales for this day was the 9.25th percentile.
