An chart for a normally distributed random variable has control limits set at ±3 standard errors from the centerline.One sample mean falls outside the control limits when the process is actually under control.The probability that this happened by chance is:
A).997
B).500
C).050
D).003

Question

An  chart for a normally distributed random variable has control limits set at ±3 standard errors from the centerline.One sample mean falls outside the control limits when the process is actually under control.The probability that this happened by chance is:
A).997 
B).500 
C).050 
D).003

Quizplus · Accepted Answer

If a sample mean falls outside the control limits, it means that the value is more than 3 standard errors from the centerline. The probability of this happening by chance is given by the area in the tails of a normal distribution beyond ±3 standard errors, which is approximately 0.003 or 0.3%. Therefore, the best choice is D.

An Chart for a Normally Distributed Random Variable Has