b)

A stamping machine punches out hinge blanks from mild steel automatically. The quality inspector has determined that in a large box of hinge blanks, 89% are within the correct tolerance values with respect to their length, the remainder being either too long or too short and out of tolerance. If a random sample of 6 hinges are drawn from the box determine the probabilities that:

1. 3 of the sample hinges are out of tolerance
2. More than 3 of the sample hinges are out of tolerance
3. Less than three of the sample hinges are out of tolerance.