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Binomial Random Variable Application

Rob works in quality at a well known saw blade company. An inspector on his team has uncovered an issue with the kerf dimension on the bandsaw blade line. Rob conducts a sampling study and finds that 7% of the bandsaw blades are out of spec.

Unfortunately, a shipment of 25 bandsaw blades left the plant about 3 hours before the issue was discovered. When Rob calls his customer receiving the bandsaw blades, he learns that they are needed for a rush job. However, the customer tells Rob that he will only need 20 of the bandsaw blades right away. The remaining five would only be needed if there were a need to replace a damaged bandsaw blade.

Rob plans to send more bandsaw blades, but they will arrive a day later. He is concerned there may not be enough bandsaw blades to supply the customer's immediate needs.

For the lot of 25 bandsaw blades, what is the probability that more than 5 of the blades will be defective?

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Solution: Here we have binomial probability distribution with and
Thus, we have