A manufacturing company produces bags of PVC powder. It is known that the variat

Question

A manufacturing company produces bags of PVC powder. It is known that the variation in weight of bags produced by this process has a normal distribution about its target weight with a standard deviation of 1 kg.

1- What should the manufacturing company set as its target weight in order for 97.5% of its bags to have a weight of at least 100 kg?

2- A random sample of 20 bags was weighed with the following results in kg.

101.26 , 99.76, 98.96 , 100.36 , 98.94

98.82 , 98.51 , 100.97 , 101.04 , 100.31

98.24 , 100.58 , 100.20 , 99.28 , 99.04

99.95 , 99.34 , 99.54 , 97.89 , 97.98

3-Determine a 95% confidence interval for process’s actual average bag weight 3. A government inspector wishes to investigate the average weight of bags being produced by this manufacturing company. If a 95% confidence interval for the process’s actual average bag weight of width no more than 0.2 kg is required, what is the minimum number of bags that need to be sampled by the government inspector?

Explanation / Answer

1) for 97.5% to be above 100 kg; for 2.5% ; z=-1.96

hence correspoding target weight =100+1.96*1=101.96

2)average weight =99.5485

std error of mean =std deviation/(n)1/2 =0.2236

for 95% CI; z=1.96

hence confidence interval =sample mean -/+ z*std error =99.1102 ; 99.9868

3) for 95% ; z=1.96

margin of error E=0.2

hence sample size =(z*std deviaiton/E)2 =~97

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