Question

In: Operations Management

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He...

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is in control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

Day	Weight (ounces)
Monday	23	22	23	24
Tuesday	23	21	19	21
Wednesday	20	19	20	21
Thursday	18	19	20	19
Friday	18	20	22	20

23 What is the sample mean package weight for Thursday?

Multiple Choice

19 ounces
20 ounces
20.6 ounces
21 ounces
23 ounces

24 What is the mean of the sampling distribution of sample means when this process is in control?

Multiple Choice

18 ounces
19 ounces
20 ounces
21 ounces
22 ounces

25 If he uses upper and lower control limits of 22 and 18 ounces, on what day(s), if any, does this process appear to be out of control?

Multiple Choice

Monday
Tuesday
Monday and Tuesday
Monday, Tuesday, and Thursday
None

Solutions

Expert Solution

Answer 23 –

Sample mean package weight for Thursday = (Weight of Package 1 + Weight of Package 2 + Weight of Package 3 + Weight of Package 4) / Number of packages

= (18+19+20+19)/4

= 19 ounces

Answer 24 –

Sample means for all days using formula mentioned above–

Monday = (23+22+23+24)/4 = 23

Tuesday = (23+21+19+21)/4 = 21

Wednesday = (20+19+20+21)/4 = 20

Thursday = (18+19+20+19)/4 = 19

Friday = (18+20+22+20)/4 = 20

Mean of the sampling distribution of sample means = Sum of sample means of all days / Number of days

= (23+21+20+19+20)/5

= 20.6 = 21 ounces (rounded off)

Answer 25 – Monday

Explanation:

Upper Control Limit = 22

Lower Control Limit = 18

Sample means of Tuesday, Wednesday, Thursday and Friday falls under these limits. However, sample mean of Monday is 23 which does not fall under these limits. Therefore, on Monday process appears to be out of control.

keosha answered 2 weeks ago

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