Question 347795: A manufacture claims that 5% of the finished items coming off an assembly line each dat are defective. A total of 5,000 items are produced a day, and 3 are randomly selected and inspected.
a. If the manufacturer's claim is correct, what is the probability all 3 randomly selected items are defective?
b. If all 3 randomly selected items are defective, would you infer the manufacturer's claim is incorrect? why?
c. if the manufacturer's claim is correct, what is the probability none of the 3 items are defective?
d. If none of the 3 items are defective, would you infer that the manufacturer's claim is incorrect? why?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacture claims that 5% of the finished items coming off an assembly line each day are defective. A total of 5,000 items are produced a day, and 3 are randomly selected and inspected.
---------------------
a. If the manufacturer's claim is correct, what is the probability all 3 randomly selected items are defective?
(0.05)^3 = 0.000125
--------------------
b. If all 3 randomly selected items are defective, would you infer the manufacturer's claim is incorrect?
why?
No; the probability that would happen is extremely low.
The defect rate is probably higher.
----------------------
If the manufacturer's claim is correct, what is the probability none of the 3 items are defective?
---
0.95^3 = 0.8574
-----------------
d. If none of the 3 items are defective, would you infer that the manufacturer's claim is incorrect?
why?
His claim has not really been tested. You would have no reason to
doubt it.
===================
Cheers,
Stan H.
|
|
|
