A soft drink company has recently received customer complaints about its one-lit

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 1.015 liters of beverage on average, with a standard deviation of 0.15 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 0.997 liters. Find the probability of observing a sample mean of 0.997 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.

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean of the sampling distribution ( x ) = 1.015
standard Deviation ( sd )= 0.15/ Sqrt ( 50 ) =0.0212
sample size (n) = 50
P(X > 0.997) = (0.997-1.015)/0.15/ Sqrt ( 50 )
= -0.018/0.021= -0.8485
= P ( Z >-0.8485) From Standard Normal Table
= 0.8019,
P(X < = 0.997) = (1 - P(X > 0.997)
= 1 - 0.80193 = 0.19807

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