In: Statistics and Probability
A factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random.
a) Find the probability that there are at most 2 defective components in the box.
b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.
Answer:
Given that,
A factory produces components of which 1% are defective.
The components are packed in boxes of 10.
A box is selected by random.
i.e,
n=10
p=0.01
q=1-p
=1-0.01
q=0.99
Where,
(a).
Find the probability that there are at most 2 defective components in the box:
:
=0.9044+0.0914+0.0019
=0.9977
(b).
Use a suitable approximation to find the probability of having at most 3 defectives (inclusive 3 cases) components out of 250:
i.e,
n=250, p=0.01 and q=0.99
:
=0.0811+0.2048+0.2574+0.0215
=0.5648