Question

A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz. Determine three sigma control limits for an x-bar (mean) chart assuming a sample size of 10. Group of answer choices UCL

Answer 1

Upper Control Limit = 6.03 oz

Lower Control Limit = 5.97 oz

Explanation:

Given - A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz.

To find - Determine three sigma control limits for an x-bar (mean) chart assuming a sample size of 10.

Proof -

Given that,

μ = 6

σ = 0.01

Z value for 3 sigma process = 3

Now,

Control limits are - μ ± Zσ

Now,

Upper Control limit (UCL) = μ + Zσ

And

Lower Control limit (LCL) = μ - Zσ

Now,

UCL = 6 + 3( 0.01 )

= 6 + 0.03

= 6.03

⇒UCL =6.03 oz

Now,

LCL = 6 - 3( 0.01)

= 6 - (0.03)

= 6 - 0.03

= 5.97

⇒LCL =5.97 oz

∴ we get

Upper Control Limit = 6.03 oz

Lower Control Limit = 5.97 oz