The mean of the sample means and the pooled standard deviation of 40 samples of size 9 taken from a production process under control are ,and S = 12,respectively.The lower control limit and the upper control limit of the 3-sigma chart are 408 and 432,respectively.

Question

The mean of the sample means and the pooled standard deviation of 40 samples of size 9 taken from a production process under control are  ,and S = 12,respectively.The lower control limit and the upper control limit of the 3-sigma  chart are 408 and 432,respectively.

Quizplus · Accepted Answer

Since the sample means are normally distributed and the lower control limit (LCL) and upper control limit (UCL) of the 3-sigma chart are given by:

LCL = X̄ - 3S/√n
UCL = X̄ + 3S/√n

where X̄ is the mean of the sample means, S is the pooled standard deviation and n is the sample size.

Substituting the given values, we get:

LCL = 11.78 - 3(12)/√9 = 2
UCL = 11.78 + 3(12)/√9 = 22.56

Therefore, the LCL and UCL of the 3-sigma chart are 2 and 22.56, respectively. Since 408 and 432 are not equal to the calculated LCL and UCL, the given statement is false.

The Mean of the Sample Means and the Pooled Standard