12. Of the bolts manufactured for a certain application, 85% meet the length specification and can be use immediately, 10% are too long and can be used after being cut, and 5% are too short and must be scrappe Eight bolts are selected at random. a What is the probability that one or more is too short? b What is the probability that seven or more are not too short? c What is the probability that more than three are either too long or too short? d What is the probability that exactly six are either too long or too short?

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### Problem 12: Bolt Length Specification

Of the bolts manufactured for a specific application, we have the following distribution regarding their length:

- **85%** meet the length specification and can be used immediately.
- **10%** are too long but can be used after trimming.
- **5%** are too short and must be discarded.

From this batch, **eight bolts** are selected at random. Analyze the probabilities for the following scenarios:

**a.** What is the probability that one or more bolts are too short?

**b.** What is the probability that seven or more bolts are not too short?

**c.** What is the probability that more than three bolts are either too long or too short?

**d.** What is the probability that exactly six bolts are either too long or too short?
Transcribed Image Text:### Problem 12: Bolt Length Specification Of the bolts manufactured for a specific application, we have the following distribution regarding their length: - **85%** meet the length specification and can be used immediately. - **10%** are too long but can be used after trimming. - **5%** are too short and must be discarded. From this batch, **eight bolts** are selected at random. Analyze the probabilities for the following scenarios: **a.** What is the probability that one or more bolts are too short? **b.** What is the probability that seven or more bolts are not too short? **c.** What is the probability that more than three bolts are either too long or too short? **d.** What is the probability that exactly six bolts are either too long or too short?
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