Question

In: Statistics and Probability

Wholesale of electronic chips receives products from two factories, factory A provides 60% Of the goods...

Wholesale of electronic chips receives products from two factories, factory A provides 60%
Of the goods and Factory B supplies 40% of the goods.
From past experience it is known that 20% of the chips of plant A are defective.
It is also known that 50% of all defective chips are supplied by plant B.

A. What percentage of Factory B's chips are defective?

B. What is the probability that a chip that is found to be in good condition is supplied by plant B?
third

C. One after the other, screws supplied from Factory B are sampled. What is the span and variance of the number of chips
That they will have to check until the first invalid is found?

D. Sample 100 chips at random, what is the probability that at least 36 of them are normal chips
Provided by Factory B?

Solutions

Expert Solution

The given data can be summarized in a table :

Defective Not defective Sum
Factory A 20% of 0.60 = 0.12 0.48 0.60
Factory B 0.12 0.28 0.40
Sum 0.24 0.76 1

A. The percentage of chips from factory B which are defective is

= (0.12/0.40) * 100

= 30%

B. The probability that a chip in good condition is supplied by factory B is

= 0.28/0.76

= 0.3684

C. The probability that a chip out of factory B will be invalid is = 0.30 (calculated earlier)

The expected number of chips that they will have to check until the first invalid chip is found is

The variance of the number of chips that they will need to check until the first invalid chip is found is

D. The probability that a random chip is normal and from factory B is = 0.28 (from the table)

The probability that at least 36 of the 100 randomly chosen chips are from factory B and normal is

Thank You!! Please Upvote!!

orchestra answered 2 years ago
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