In a random sample of 100 parts ordered from vendor \(A\), 12 were defective. In a random sample of 200 parts ordered from vendor \(B\), 10 were defective.

a. Estimate the proportion of parts from vendor \(A\) that are defective, and find the uncertainty in the estimate.

b. Estimate the proportion of parts from vendor \(B\) that are defective, and find the uncertainty in the estimate.

c. Estimate the difference in the proportions, and find the uncertainty in the estimate.

Equation Transcription:

Text Transcription:

A

B

Answer :

Step 1 of 4:

Given, we have two sample size, vender A ordered random sample of 100 parts, in that 12 were defectives.

vender B ordered random sample of 200 parts, in that 10 were defectives.

Let X follows binomial distribution with probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Where,

n = sample size

= 5

x = random variable

p = probability of success

q = 1 - p (probability of failure)

The goal of the problem is

- We have to find the proportion of parts from part A that are defective and the uncertainty in the estimate.
- We have to find the proportion of parts from part B that are defective and the uncertainty in the estimat.
- We have to find the difference in the proportions, and the uncertainty in the estimate.