Question 1186973
population mean is 1.015 liters
population standard deviation is .14 liters.


sample size is 50
sample mean is .993 liters.


standard error = population standard deviation divided by square root of sample size = .14 / sqrt(50) = .0198 rounded to 4 decimal places.


z-score = (x - m) / s
x is the sample mean
m is the population mean
s is the standard error.


z = (.993 -  1.015) / .0198 = -1.1111 rounded to 4 decimal places.


area to the left of that z-score = .1333 rounded to 4 decimal places.


that's the probability of observing a sample mean of 0.993 liters or less in a sample of 50 bottles, if the beverage dispensing unit functions properly.