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

Answer:

0.5160

Step-by-step 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)

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