Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed: Sample Mean Range Sample Mean Range

1 3.06 .42 4 3.13 .46

2 3.15 .50 5 3.06 .46

3 3.11 .41 6 3.09 .45

Factors for three-sigma control limits for x and R charts FACTORS FOR R CHARTS

Number of Observations in Subgroup, n Factor for x Chart, A2 Lower Control Limit, D3 Upper Control Limit, D4

2 1.88 0 3.27

3 1.02 0 2.57

4 0.73 0 2.28

5 0.58 0 2.11

6 0.48 0 2.00

7 0.42 0.08 1.92

8 0.37 0.14 1.86

9 0.34 0.18 1.82

10 0.31 0.22 1.78

11 0.29 0.26 1.74

12 0.27 0.28 1.72

13 0.25 0.31 1.69

14 0.24 0.33 1.67

15 0.22 0.35 1.65

16 0.21 0.36 1.64

17 0.20 0.38 1.62

18 0.19 0.39 1.61

19 0.19 0.40 1.60

20 0.18 0.41 1.59

a. Using the factors in the above table, determine upper and lower limits for mean and range charts. (Round your intermediate calculations and final answers to 4 decimal places.) Upper limit for mean Lower limit for mean Upper limit for range Lower limit for range

b. Is the process in control?

Yes / No