Final answer:
To determine the probability of there being more than one defective part in a batch of 26 from a manufacturing facility, calculate the binomial probabilities for 0 and 1 defective item and subtract their sum from 1. It is often easier to use a calculator or software to perform these computations.
Step-by-step explanation:
To find the probability of having more than one defective part in a random batch of 26 parts at a manufacturing facility, we can use the binomial probability formula. The probability of a part being defective is 11% (or 0.11), and the probability of a part not being defective is 89% (or 0.89). We need to calculate the probability of having 0 or 1 defective part and then subtract this from 1 to find the probability of having more than 1 defective part.
Let X be the random variable that represents the number of defective parts in a batch of 26. The probability of having exactly x defective parts is given by:
P(X = x) = (26 choose x) * (0.11)^x * (0.89)^(26-x)
We calculate:
P(X = 0)
P(X = 1)
Then we find:
P(more than one defective) = 1 - [P(X = 0) + P(X = 1)]
For calculations for P(X = 0) and P(X = 1), it is often easier to use a calculator or software, as working out the combinations and powers can become quite lengthy.
Finally, the probability sought will be the combined probability of having 2 to 26 defective parts in the batch, which is the complement of having at most one defective part.