Question

A control chart indicates that the current process fraction nonconforming is 0.02. If 50 items are inspected each day, what is the probability of detecting a shift in the fraction nonconforming to 0.04 on the first day after the shift? By the end of the third day following the shift?

Answer 1

To find the probability of detecting a shift in the fraction nonconforming from 0.02 to 0.04, we can use the geometric distribution. The probability of detecting a shift on the first day is 0.02. The probability of detecting a shift by the end of the third day is 0.0584, or 5.84%.

Step-by-step explanation:

To find the probability of detecting a shift in the fraction nonconforming from 0.02 to 0.04, we can use the geometric distribution. The geometric distribution is used to model the number of trials needed to achieve a success.

Since the current process fraction nonconforming is 0.02, the probability of a nonconforming item is also 0.02. So, the probability of detecting a shift on the first day is 0.02.

To find the probability of detecting a shift by the end of the third day, we can find the complement of the probability of not detecting a shift in 3 days. The probability of not detecting a shift in 3 days is (1 - 0.02)^3 = 0.9416.

So, the probability of detecting a shift by the end of the third day is 1 - 0.9416 = 0.0584, or 5.84%.