Posted by **Probability that bottle has flaw!!!!!?** on Saturday, October 1, 2011 at 4:49pm.

A quality-control program at a plastic bottle production line involves

inspecting finished bottles for flaws such as microscopic holes. The proportion of bottles that actually

have such a flaw is only 0.0002. If a bottle has a flaw, the probability is 0.995 that it will fail the

inspection. If a bottle does not have a flaw, the probability is 0.99 that it will pass the inspection (use

Bayes’s Rule).

a. If a bottle fails inspection, what is the probability that it has a flaw?

b. Which of the following is the more correct interpretation of the answer to part(a)?

i. Most bottles that fail inspection do not have a flaw.

ii. Most bottles that pass inspection do have a flaw.

c. If a bottle passes inspection, what is the probability that it does not have a flaw?

d. Which of the following is the more correct interpretation of the answer to part(c)?

i. Most bottles that fail inspection do have a flaw.

ii. Most bottles that pass inspection do not have a flaw.

e. Explain why a small probability in part (a) is not a problem, so long as the probability in part (c)

is large.

## Answer this Question

## Related Questions

- science - for my intro i got a 'Water is the elixir of life'and i got lota of ...
- Statistics - A machine is used to fill soda bottles in a factory. The bottles ...
- Probabability - You are in charge of quality control on a line which fills ...
- Science - The bottled water industry has become an enormous, multi-billion ...
- MAT 115 - Julio works as a quality control expert in a beverage factory. The ...
- Basic Math with Geometry - Julio works as a quality control expert in a beverage...
- math - Business and finance. Julio works as a quality control expert in a ...
- Math - Here is my question: Julio works as a quality control expert in a ...
- Statistics - A brewery's filling machine is adjusted to fill bottles with a mean...
- Math - Here is my question; Business and finance. Julio works as a quality ...