Unknown to a quality-control inspector, 20% of a very large shipment of electric switches are defective. The inspector has been told to reject the shipment if, in a sample of 15 switches, 2 or more are defective. The probability that the shipment will be rejected is:
I do not know how to work this problem. I need the steps on what to calculate
To calculate the probability that the shipment will be rejected, we need to use the concept of binomial probability. Here are the steps to solve this problem:
Step 1: Determine the probability of a defective switch.
Given that 20% of the switches are defective, the probability of a switch being defective is 0.20 (or 20/100).
Step 2: Determine the sample size and the number of defective switches in the sample.
In this problem, the sample size is 15 switches. We are interested in the probability of having 2 or more defective switches in the sample.
Step 3: Calculate the probability of having exactly 2, 3, 4, ..., up to the maximum number of defective switches allowed.
We need to calculate the probability of 2 defective switches, 3 defective switches, and so on, up to 15 defective switches. Then we sum up all these probabilities.
Step 4: Calculate the probability of rejection.
To find the probability that the shipment will be rejected, we need to calculate the cumulative probability of having 2 or more defective switches. We sum up all the individual probabilities from Step 3.
I will now calculate the probability of rejection using these steps.