Given that 20 samples are taken in a control chart initiative, the probability that 5 consecutive samples are below the center line in an R- or x-bar chart is _____.
A) 0.02500
B) 0.03125
C) 0.06250
D) 0.25000

Question

Quizplus · Accepted Answer

The probability of a single point being below the centerline is 0.5 (assuming the process is in control and centered on the centerline). 
The probability of 5 consecutive points being below the centerline is (0.5)^5 = 0.03125. 
Since there are 16 groups of 5 consecutive samples (20-5+1), we need to multiply 0.03125 by 16 to get the total probability of observing 5 consecutive samples below the centerline. 
This gives us 0.03125 x 16 = 0.5. So the answer is B.

Given That 20 Samples Are Taken in a Control Chart