Question

As a quality control engineer, you’re examining the performance of two of the suppliers (A and B) of a key sub-assembly in a system that your factory produces. You purchased a total of 387 batches of parts from Supplier A and 283 batches from Supplier B. When batches arrive, you inspect them to determine if they meet quality standards: batches either “meet” or “fail to meet” standards. The past quality data that you’ve collected appears below.

a. From Supplier A, you pull a random sample of five sub-assemblies. What is the probability that fewer than two fail to meet standards?

b. From Supplier B, you pull a random sample of three sub-assemblies. What is the probability that all three meet standards?

c. From the collection of sub-assemblies that fail to meet standards, you pull a random sample of six sub-assemblies. What is the probability that only one comes from Supplier B?

	Meet Standards	Fail to Meet Standards
Supplier A	346	41
Supplier B	245	38

Answer 1

	Meet Standards	Fail to meet Standards	Total
Supplier A	346	41	387
Supplier B	245	38	283
Total	591	79	670

a) Here n = 5

p = probability that fail to meet standards from supplier A.

= 0.06

Here we need to find, the probability that fewer than two fail to meet standards, p ( x < 2 ) .

Using binomial distribution,

p ( X = x ) = ⁿC_x * p^x * ( 1 - p)^n-x

So, p ( x < 2 ) = p ( x = 0 ) + p ( x =1 )

= ⁵C₀ *0.06⁰ * ( 1 - 0.06)^5-0  + ⁵C₁ * 0.06¹ * ( 1 - 0.06)^5-1

= 0.7339 + 0.2342

= 0.9681

2) Here n = 3,

p = probability that meet standards from supplier B.

  

= 0.37

Here we need to find, the probability that all three meet standards.

p ( x = 3 ) = ³C₃ * 0.37³ * ( 1 - 0.37)^3-3

= 0.0507

3) Here a random sample of six sub-assemblies selected from , the collection of 79 sub-assemblies that fail to meet standards.

Out of 6 one come from supplier B and 5 come from supplier A.

So required probability is given by,

= 0.102