A teller at a drive-up window at a bank had the following service times (in minutes) for 20 randomly selected customers:SAMPLE12344.54.64.54.74.24.54.64.64.24.44.44.84.34.74.44.54.34.34.64.9 a.Determine the mean of each sample.b.If the process parameters are unknown, estimate its mean and standard deviation.c.Construct control charts for means and ranges using Table 10.3. Are any samples beyond the control limits? If so, which one(s)?d.If the process has a known mean of 4.4 and a known standard deviation of .18, what would three-sigma control limits be for a mean chart? Are any sample means beyond the control limits? If so, which one(s)?

Question
Asked Sep 27, 2019
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A teller at a drive-up window at a bank had the following service times (in minutes) for 20 randomly selected customers:

SAMPLE

1

2

3

4

4.5

4.6

4.5

4.7

4.2

4.5

4.6

4.6

4.2

4.4

4.4

4.8

4.3

4.7

4.4

4.5

4.3

4.3

4.6

4.9

 

a.

Determine the mean of each sample.

b.

If the process parameters are unknown, estimate its mean and standard deviation.

c.

Construct control charts for means and ranges using Table 10.3. Are any samples beyond the control limits? If so, which one(s)?

d.

If the process has a known mean of 4.4 and a known standard deviation of .18, what would three-sigma control limits be for a mean chart? Are any sample means beyond the control limits? If so, which one(s)?

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Expert Answer

Step 1

a)

Determine the mean of each sample:

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B А D Sample 1 2 2 3 1 4 4.5 4.5 4.7 4.6 4.2 4.5 4.6 4.6 4 5 4.2 4.8 4.4 4.4 4.3 4.7 4.5 6 4.4 7 4.3 4.3 4.5 4.6 4.9 4.3 8 4.7 Mean 4.5 A В C Sample 3 4.5 4.6 4.4 4.4 |4.6 8 Mean AVERAGE(B3:B7) |=AVERAGE(C3:C7)|=AVERAGE(D3:D7)|=AVERAGE(E3:E7) 1 2 1 2 4 4.6 4.5 4.4 4.7 4.3 4.7 4.6 4.8 4.5 4.9 4.5 4.2 3 4 4.2 4.3 4.3 5 7 t CO et

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Step 2

b)

Determine the mean and standard deviation when the parameters are unknown:

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А B С D F G 1 Sample 1 2 2 3 4 3 4.5 4.6 4.5 4.7 4 4.2 4.5 4.6 4.6 4.4 5 4.2 4.4 4.8 6 4.3 4.7 4.4 4.5 Standard Мean deviation 7 4.3 4.3 4.6 4.9 8 Mean 4.3 4.5 4.5 4.7 4.5 0.192 B D A с E F Sample 1 4 4.7 4.6 4.8 4.5 4.9 8 Mean =AVERAGE(B3:B7)| =AVERAGE(C3:C7) |=AVERAGE(D3:D7) =AVERAGE(E3-E7)| =AVERAGE(B$:ES) =STDEV.S(B3:E7) 2 3 4.5 4.2 4.2 4.3 4.3 4.6 4.5 4.4 4.7 4.3 4.5 4.6 4.4 4.4 4.6 3 4 5 6 Standard deviation Mean

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Step 3

Determine R-bar and X-double ba...

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B E A C F Sample 1 2 1 2 3 4 4.5 3 4.5 4.6 4.7 4.2 4.5 4.6 4.6 4 5 4.2 4.4 4.4 4.8 4.4 4.3 4.7 4.5 4.3 7 4.3 4.6 4.9 8 Mean 9 Range 4.3 4.5 4.5 4.7 4.5 0.3 0.4 0.2 0.4 0.325 C A Sample 3 4.5 1 4.5 4.2 4.2 43 4.3 2 4.6 4.5 4.4 4.7 4.3 AVERAGE(C3.CT) 4 2 4.7 4.6 3 4.6 4.4 44 4.8 4.5 4.9 AVERAGE(E3E7) 5 6 4.6 7 8 MeanAVERAGE(B3 B7) |-AVERAGE(D3D7 -AVERAGE(BS:ES) Range MAX(B3B7)-MIN(B3 B7)| -MAX(C3.C7)-MIN(C3.C7 ) -MAX(D3 D7)-MIN(D3D7) | -MAX(E3E7)-MIN(E3E7) -AVERAGE(B9:E9) 9

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