Question 1203452: A study of furniture wholesales,inc regarding the payment of invoice revealed that, on the average, an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. What is the probability of selecting invoice and finding it was paid between 18 and 26 days after it was paid
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! use of the calculator at https://davidmlane.com/hyperstat/z_table.html can help answer this.
the resullt shows that the probability of getting an invoice paid between 18 and 26 days is equal to .5404.
if you want to solve this using z-scores, you would do the following.
z = (x-m)/s formula is used.
z is the z-score
x is the desired value
m is the mean
s is the standard deviation.
on the low side, the formula becomes z = (18 - 20) / 5 = -.4.
on the high side, the formula becomes z = (26 - 20) / 5 = 1.2
using the same calculaator, you would make the mean = 0 and the standard deviation = 1 and you would get probability of getting a z-score between -.2 and 1.2 = .5404.
you could also have solved it by doing the following:
low z-score = -.4
area to the left of that = .3446
high z-score = 1.2
area to the left of that = .8849
area in between = .5403.
this method could be used with the calculaator, as we just did, or it could be used with the z-score tables that provide the area to the left of the z-scores.
such a table can be found at https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf
using that table, you would find that the area to the left of a z-score of:
-.4 = .34458
2.2 = .88493
area in between would be equal to the larger area minus the smaller area = .54035.
with the calculator, you can get the answer directly from the mean and the standad deviation or with the z-score.
with the z-score, the mean is always 0 and the standad deviatioon is always 1.
with the table, you have to use the z-score.
here are the results using the calculator directly from the raw score, mean and standard deviation.
here are the results using the calculator from the z-score. with this method, the mean is always 0 and the standard deviation is always 1.
the calculator can get you the area in between directly, whether you use the raw score method or the z-score method.
with the table, you can only use the z-score and the subtraction of area to the left of the low z-score from the areaa to the left of the high z-score method.
here are the results using the calculator with the subtraction method.
this mimics what you would get using the table.
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