Question 1162233
i believe this is how it's done.
mean is 540
standard deviation is 250.
n = 13
7500 hours during the day / 13 = average of 576.9230769.
if the average exceeds that, then the total day will exceed 7500.
the standard deviation remains the same.
you're looking for the probability that the average number of customer per day exceeds 576.9230769.
find the z-score and then look up the probability in the normal distribution tables is what i think you need to do.
formula for z-score is z = (x-m)/s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
formula becomes z = (576.9230769 - 540) / 250 = .1476923077
look up a z-score of 0.15 in the z-score table to find the area to the right of that, or look up the full z-score in a z-score calculator to find the area to the right of that.
in the z-score table, you will get area to the left of .15 is equal to .55962.
the area to the right of that z-score is equal to 1 minus that = .44038.
the probability of getting a z-score greater than that z-score is the area to the right.
if you use a calculator, you can get greater accuracy.
you would look for the area to the right of a z-score of .1476923077.
you would find the area to the left of that z-score = .558707 and the ara to the right of the z-score = .441293


the table i used can be found at <a href = "https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf" target = "_blank">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>


the online calculator i used can be found at <a href = "https://www.omnicalculator.com/statistics/normal-distribution" target = "_blank">https://www.omnicalculator.com/statistics/normal-distribution</a>


the display calculator i used can be found at <a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


here's a display of the table when i used z-scores.


<img src = "http://theo.x10hosting.com/2020/071101.jpg" >


here's a display of the calculator when i used z-scores.


<img src = "http://theo.x10hosting.com/2020/071102.jpg" >


here's a display of the calculator when i used raw scores.


<img src = "http://theo.x10hosting.com/2020/071103.jpg" >


here's a visual display when i used raw scores.


<img src = "http://theo.x10hosting.com/2020/071104.jpg" >