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 months ago
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