Which of the following statements are not true?
A) One important use of control charts is to see whether some measure of location of the variable's distribution remains stable over time.
B) It is highly unlikely that for an in-control process, the sample mean will fall within 3 standard deviations $( 3 \sigma/ \sqrt { n } )$
Of the process mean $\mu .$
C) The use of control charts based on 3 standard deviation limits is traditional, but tradition is certainly not inviolable.
D) All of the above statements are true.
E) None of the above statements are true.

Question

Quizplus · Accepted Answer

EStatement B is not true because for an in-control process, it is actually highly likely (about 99.73% chance) that the sample mean will fall within 3 standard deviations $(3\sigma/\sqrt{n})$ of the process mean $\mu$. This is based on the empirical rule or 68-95-99.7 rule, which states that for a normal distribution, about 99.73% of the data falls within three standard deviations of the mean. Therefore, statement B is incorrect, making E (None of the above statements are true) also incorrect since B is not true.

Which of the Following Statements Are Not True? A) One (3σ/n)( 3 \sigma/ \sqrt { n } )(3σ/n​)

Which of the Following Statements Are Not True?
A) One $( 3 \sigma/ \sqrt { n } )$