Question

One of the assumptions underlying the theory of control charting is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Even when a process is running correctly, there is a small probability that a particular point will signal a problem with the process. Suppose that this probability is 0.07. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly? (Round your answer to three decimal places.)

Answer 1

0.5160

Explanation:

Xi:"i-th Signal"

Xi=1, False alarm

Xi=0, True error

`Y=\sum ^(10)_(i=1)Xi`

X=Ber(p=0.07)

Y=Bin(n=10, p=0.07)

`P(\displaystyle\sum_(i=1)^(10) X_i\geq 1)=1-P(\displaystyle\sum_(i=1)^(10) X_i=0)=1-P(Y=0)=1-(1-0.07)^(10)=0.5160`