Answer: the probability of rejecting the lot is 0.68
Explanation:
Assuming a binomial probability distribution, the formula for binomial distribution is expressed as
P(x = r) = nCr × q^(n - r) × p^r
Where
n = number of samples
p = probability that an event will happen.
q = probability that an event will not happen.
From the information given,
n = 20
If an incoming lot is 10 percent defective, it means that
p = 10/100 = 0.1
q = 1 - p = 1 - 0.1 = 0.9
If 2 or less defective bolts are discovered, the lot will be rejected. The probability of rejecting the lot would be
P(x lesser than or equal to 2)
P(x lesser than or equal to 2) =
P(x = 0) + P(x = 1) + P(x =2)
P(x = 0) = 20C0 × 0.9^(20 - 0) × 0.1^0 = 0.12
(x = 1) = 20C1 × 0.9^(20 - 1) × 0.1^1 = 0.12 = 0.27
(x = 2) = 20C2 × 0.9^(20 - 2) × 0.1^2 = 0.12 = 0.29
P(x lesser than or equal to 2) = 0.12 + 0.27 + 0.29 = 0.68