A local company makes snack-size bags of potato chips. The company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the population of filling weights is normally distributed with a standard deviation of 0.1 ounce. The company periodically weighs samples of 10 bags to ensure the proper filling process. The last five sample means, in ounces, were 1.99, 2.02, 2.07, 1.96, and 2.01. Is the production process under control?
Yes, because the sample means show a downward trend.
No, because the sample means fall within the upper and lower control limits.
No, because the sample means show a downward trend.
Yes, because the sample means fall within the upper and lower control limits.
To answer this question, we need to find the upper and lower control limits
it is given that mean = 2, population standard deviation = 0.1 and sample size is n = 5
So, sample standard deviation = SD/sqrt{n}
where SD=0.1 and n = 5
this implies
sample standard deviation = 0.1/sqrt{5} = 0.04
Upper control limit = mean + 3(sample standard deviation)
= 2 + (3*0.04)
=2.12
and
lower control limit = mean - 3(sample standard deviation)
= 2 - (3*0.04)
=1.88
it is clear that none of the 5 sample values are outside these control limits
Therefore, we can say that the sample means fall within the upper and lower control limits
option D is correct
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