Question

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 under control, package weight is normally distributed with a mean of twenty 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

What are the upper and lower control limits for these data?

a. UCL = 22.644 LCL = 18.556
b. UCL = 22.700 LCL = 18.500
c. UCL = 22.755 LCL = 18.642
d. UCL = 21.814 LCL = 19.300

Answer 1

a. UCL = 22.664 LCL = 18.556

Step-by-step explanation:

The sample mean for the given data is :

( 23 + 20 + 19 + 20 + 21 ) / 5 = 20.6

Upper control limit is :

Sample mean + standard deviation

20.6 + 2 = 22.6

Lower Control Limit is :

Sample mean - Standard Deviation

20.6 - 2 = 18.6