Negative Binomial Distribution

**2. Experience tells you that 5% of pumps (of a given make and model) are defective. Use the negative binomial distribution to answer the questions below. **

**a. What is the probability that the next pump you order is good (has no defects)? [You don’t need the negative binomial for this part.]**

5 out of 100 times, the pump you will buy is defective, so, by this trend, the remaining 95 times out of 100 (on average), your pump should be fully functional. In other words, you have a 95% chance of purchasing a “good” pump.

**b. What is the probability of having to order 5 pumps to get 5 good ones? **I know it's .774, but how do I show this using negative binomial distribution?

**c. What is the probability of having to order 6 pumps to get 5 good ones?**

**d. What is the probability of having to order 7 pumps to get 5 good ones?**

**e. How many pumps should you order to have at least a 95% chance of getting 5 good ones?**

**f. How many pumps should you order to have at least a 99% chance of getting 5 good ones? **