A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius. Inspectors take weekly samples for 5 weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below. How many points are outside the control limits?
A) 1
B) 2
C) 3
D) 4

Question

A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius. Inspectors take weekly samples for 5 weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below.  How many points are outside the control limits?
A) 1 
B) 2 
C) 3 
D) 4

Quizplus · Accepted Answer

The control limits for the X̄ chart can be calculated as:
Upper Control Limit (UCL) = μ + 3(σ/√n) = 5 + 3(0.3/√8) = 5.29
Lower Control Limit (LCL) = μ - 3(σ/√n) = 5 - 3(0.3/√8) = 4.71

Looking at the table, we can see that sample means 2, 3, and 4 are outside the control limits. Therefore, there are 3 points outside the control limits. Hence, the answer is (C) 3.

A Packaging Company Strives to Maintain a Constant Temperature for Its