Which of the following statements are true?
A) The p control chart for the fraction of items not conforming to specifications is based on the binomial probability distribution.
B) The c control chart for the number of defectives is based on the Poisson probability distribution.
C) If the random variable X has a binomial distribution with parameters n and p, then when p is small the transformation $Y = h ( X ) = \sin ^ { - 1 } ( \sqrt { X / n } )$
Is recommended and that the points $y _ { 1 } , y _ { 2 } , \ldots , y _ { n }$
Should be used to construct the p chart.
D) If the random variable X has a Poisson distribution with parameter $\lambda ,$
And $\lambda$
Is small, then the transformation $Y = h ( X ) = 2 \sqrt { X }$
Is recommended and that the points $y _ { 1 } , y _ { 2 } , \ldots \ldots$
Should be used to construct the c chart.
E) All of the above statements are correct

Question

Quizplus · Accepted Answer

- A) True, the p control chart is indeed based on the binomial distribution, which is used for the fraction of nonconforming items.- B) True, the c control chart is based on the Poisson distribution, which is appropriate for counting defects.- C) True, the arcsine square root transformation is a recommended transformation for binomial data, especially when dealing with proportions.- D) True, the square root transformation is a common recommendation for Poisson-distributed data, particularly when the mean of the distribution is small. This transformation helps stabilize the variance.

Which of the Following Statements Are True? A) the P Y=h(X)=sin⁡−1(X/n)Y = h ( X ) = \sin ^ { - 1 } ( \sqrt { X / n } )Y=h(X)=sin−1(X/n​)

Which of the Following Statements Are True?
A) the P $Y = h ( X ) = \sin ^ { - 1 } ( \sqrt { X / n } )$