11. (8pts) A manufacturer of metal pistons claims that on average, only 10% of their pistons are bad
(either oversize or undersize). When the pistons are delivered to a local store, a quality control
staff will randomly select 9 pistons, and measure if they are oversize or undersize. If he sees 3 or
more pistons are bad, they will reject the delivery.
What is the probability that the staff will reject the delivery, if we assume the fault rate for
the pistons is 0.10?
$C_9^0 = 1$, $C_9^1 = 9$, $C_9^2 = 36$, $C_9^3 = 84$, $C_9^4 = 126$, $C_9^5 = 126$, $C_9^6 = 84$, $C_9^7 = 36$, $C_9^8 = 9$, $C_9^9 = 1$
Hint: Define variable X = # of pistons that are either oversize or undersize out of those 9
pistons, identify the distribution of x from Binomial setting.
Complement Rule: P (Not A) = 1 - P (A)
From Complement Rule: P ( X ? 3) = 1-P (X < 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)].