SOLUTION: A global financial institution transfers a large data file every evening from offices around the world to its London headquarters. Once the file is recieved, it must be cleaned and

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Question 1182192: A global financial institution transfers a large data file every evening from offices around the world to its London headquarters. Once the file is recieved, it must be cleaned and partitioned before being stored in a company's data warehouse. Each file is the same size and the time required to transfer, clean, and partition a file is normally distributed, with a mean of 1.5 hours and standard deviation of 15 minutes. If a manager must be present until 85% of the files are transferred, cleaned, and partitioned, how long will the manager need to be there?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 1.5 hours and standard deviation is 15 minutes = .25 hours.
z-score for 85% area under the normal distribution curve to the left of it is equal to 1.03643338.
z-score formula is:
z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
solve for raw score to get:
x = z * s + m = 1.03643338 * .25 + 1.5 = 1.759108345 hours.
that's how long the manager must be present.
this is what it looks like on the statistical calculator found at https://davidmlane.com/hyperstat/z_table.html