Question 1186973: A soft drink company has recently received customer complaints about its one-liter-sized soft drink products. Customers have been claiming that the one-liter-sized products contain less than one liter of soft drink. The company has decided to investigate the problem. According to the company records, when there is no malfunctioning in the beverage dispensing unit, the bottles contain 1.015 liters of beverage on average, with a standard deviation of 0.14 liters. A sample of 50 bottles has been taken to be measured from the beverage dispensing lot. The mean amount of beverage in these 50 bottles was 0.993 liters. Find 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.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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