Marble Inc.makes countertops from a variety of high-end materials.To monitor the quality of its production processes the company randomly selects one countertop and counts the number of blemishes.The results for ten samples are shown below: Given the sample information above,the UCL using sigma = 3 for this process would be
A)36
B)32
C)30
D)28

Question

Marble Inc.makes countertops from a variety of high-end materials.To monitor the quality of its production processes the company randomly selects one countertop and counts the number of blemishes.The results for ten samples are shown below:  Given the sample information above,the UCL using sigma = 3 for this process would be
A)36 
B)32 
C)30 
D)28

Quizplus · Accepted Answer

To calculate the UCL using sigma = 3, we need to use the formula:

UCL = X̄ + 3σ

where X̄ is the average number of blemishes and σ is the standard deviation.

Using the data provided, we can calculate X̄ and σ as follows:

X̄ = (9+12+7+10+13+11+15+8+6+14)/10 = 10.5

σ = √[((9-10.5)²+(12-10.5)²+...+(14-10.5)²)/9] = 2.87

Substituting these values into the formula, we get:

UCL = 10.5 + 3(2.87) = 19.1

Therefore, the closest answer choice is D (28).