Question

In: Statistics and Probability

A factory produces components of which 1% are defective. The components are packed in boxes of...

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.

Solutions

Expert Solution

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

orchestra answered 2 years ago
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