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 0.14 liters of beverage on average, with a standard deviation of 70 bottles has been taken to be measured from the beverage dispensing lot. The mean amount of beverage in these 70 bottles was 0.985 liters. Find the probability of observing a sample mean of 0.985 liters or less in a sample of 70 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 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	1.02
std deviation   =σ=	0.14
sample size       =n=	70
std error=σx̅=σ/√n=	0.01673

probability of observing a sample mean of 0.985 liters or less in a sample of 70 bottles :

probability =P(X<0.985)=(Z<0.985-1.02)/0.017)=P(Z<(-2.09)=0.018