Question

Red top cab company receives multiple complaints per day about driver behavior. over 9 days the owner recorded the number of calls to be 3, 0, 8, 9, 6, 7, 4, 9, and 8. what is the upper control limit and lower control limit for the 3-sigma c-chart?

a. 13.35; 0
b. 8.45; .35
c. 24.00; 14.00
d. 13.35; -1.34
e. 9.03; .9

Answer 1

The upper control limit (UCL) and lower control limit (LCL) for the 3-sigma c-chart, based on the average number of complaints per day, are 13.35 and 0, respectively. Therefore, the correct option is A.

Step-by-step explanation:

To determine the upper control limit (UCL) and lower control limit (LCL) for the 3-sigma c-chart, we need to first calculate the average number of complaints received per day based on the data provided.

The total number of complaints received over 9 days is 3 + 0 + 8 + 9 + 6 + 7 + 4 + 9 + 8 = 54 complaints. To find the average, we divide this by the number of days: 54 complaints / 9 days = 6 complaints per day on average. This average is represented by μ (mu).

To calculate the control limits, we use the formulas:

• UCL = μ + 3σ
• LCL = μ - 3σ

Since we are working with a c-chart, which is used for count data, the standard deviation σ (sigma) is the square root of μ. Therefore, σ = √6 ≈ 2.45.

Now, we can calculate the UCL and LCL:

• UCL = 6 + 3(2.45) = 6 + 7.35 = 13.35
• LCL = 6 - 3(2.45) = 6 - 7.35 = -1.35

However, since we cannot have a negative number of complaints, the LCL is adjusted to 0. Therefore, the UCL and LCL for the 3-sigma c-chart are 13.35 and 0, respectively.