tps//www-awh.aleks.com/alekscgi/x/lslexe/1o u-IgNslkasNwBD8A9PVVI97mMVKlycKM6240

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tps//www-awh.aleks.com/alekscgi/x/lslexe/1o u-IgNslkasNwBD8A9PVVI97mMVKlycKM6240AaXEieTgw-85PnáZe3oj9qFqAR20haleW3N96Y1MBmuP Math 063-109 Elementary Statistics-TTh 12. Homework 7(Sections ?-7A-180f20 10 12 14 15 20 A soft drink company has recently received customer complaints about its one-liter-sized soft drink products. Customers have been claiming that the 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 0.15 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 botties, 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

? = 1.02, ? = 0.15, n = 60, x-bar = 0.997

z = (x-bar - ?)/(?/?n)

z = (0.997 - 1.02)/(0.15/?60) = -1.1877

We can use z-table to find out the probability, please use linear interpolation to find out the exact value.
P(x-bar ? 0.993) = P(z < -1.1877) = 0.1175

Answer: 0.1175

Let me explain how to get values from z table and use linear interplation:

just google z table and you should abe able to find the z table with probability values:

in our case: by reading the table we can probability values at following z values:

at z = -1.18 , p = 0.1190

at z = -1.19 , p = .1170

we want to find the value of p at -1.1877 which lies betweeb -1.18 and 1.19

we can linear interpolation, lets divide the p values between z=-1.18 and z=-1.19 into 100 equal parts:

as we know value of p is decreasing as z goes from -1.18 to -1.19, we can calculate p at -1.1877 as :

P(z = -1.1877) = 0.1190 - (0.1190-0.1170)*77/100 = 0.11746 = 0.1175(round off to four decimal points)

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