As part of quality control, you carry out inspection of your product on a weekly basis. You set a quality standard that the weight of a package must be on average 250 grams. From the past data, you know that the standard deviation is 40 grams. a) Based on the information above, what is the probability that a randomly selected package is weighted 300 grams or more? b) Suppose 16 packages are inspected, what is the probability that the sample mean will be between 245 and 265 grams? c) You want to set up the upper limit and the lower limit of package weight such that if the sample mean exceeds the upper limit or falls below the lower limit, you would take that the production does not run properly and the machines must be inspected. What should be the upper limit a
As part of quality control, you carry out inspection of your product on a weekly basis.
You set a quality standard that the weight of a package must be on average 250
grams. From the past data, you know that the standard deviation is 40 grams.
a) Based on the information above, what is the probability that a randomly selected
package is weighted 300 grams or more?
b) Suppose 16 packages are inspected, what is the probability that the sample
will be between 245 and 265 grams?
c) You want to set up the upper limit and the lower limit of package weight such that
if the sample mean exceeds the upper limit or falls below the lower limit, you would
take that the production does not run properly and the machines must be
inspected. What should be the upper limit and the lower limit in terms of grams
when you set the probability of sample mean to be over the upper limit and below
the upper limit at 5%.
d) Suppose that you carry out the inspection for three consecutive weeks, each week
with a sample of 16 packages and you observe that in those three weeks, the mean
weight exceeds the limit set. Is this a likely outcome? What conclusion can you
draw from this outcome?
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