Question

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 1.02 liters of beverage on average, with a standard deviation of 0.16 liters. A sample of 60 bottles has been taken to be measured from the beverage dispensing lot. The mean amount of beverage in these 60 bottles was 0.997 liters. Find the probability of observing a sample mean of 0.997 liters or less in a sample of 60 bottles, if the beverage dispensing unit functions properly.

Answer 1

It is known that, under large sample size (n>30) due to Central Limit Theorem,

here, n=60

Statement of Central Limit Theorem
The Central Limit Theorem, states that, for a population with mean and variance , then, under sufficiently large sample, the sample mean is approximately Normally distributed.

We are to find






I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)