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Quality Control After constructing a new manufacturing
Chapter 6, Problem 18BSC(choose chapter or problem)
Problem 18BSC
Quality Control After constructing a new manufacturing machine, five prototype integrated circuit chips are produced and it is found that two are defective (D) and three are acceptable (A). Assume that two of the chips are randomly selected with replacement from this population.
a. After identifying the 25 different possible samples, find the proportion of defects in each of them, then use a table to describe the sampling distribution of the proportions of defects.
b. Find the mean of the sampling distribution.
c. Is the mean of the sampling distribution (from part (b)) equal to the population proportion of defects? Does the mean of the sampling distribution of proportions always equal the population proportion?
Questions & Answers
QUESTION:
Problem 18BSC
Quality Control After constructing a new manufacturing machine, five prototype integrated circuit chips are produced and it is found that two are defective (D) and three are acceptable (A). Assume that two of the chips are randomly selected with replacement from this population.
a. After identifying the 25 different possible samples, find the proportion of defects in each of them, then use a table to describe the sampling distribution of the proportions of defects.
b. Find the mean of the sampling distribution.
c. Is the mean of the sampling distribution (from part (b)) equal to the population proportion of defects? Does the mean of the sampling distribution of proportions always equal the population proportion?
ANSWER:Answer :
Step 1 of 1 :
Given Quality Control After constructing a new manufacturing machine, five prototype integrated circuit chips are produced and it is found that two are defective (D) and three are acceptable (A).
We assume that two of the chips are randomly selected with replacement from this population.
Given 25 different possible samples.
Now we have to find the proportion of defects in each of them, then use a table to describe the sampling distribution of the proportions of defects.
The sample proportion is the number of defects (a and b represent defects machine) in the sample divided by the number of machines.
Assign every sample as an equal probability.
Add the probabilities for each sample value.
Then the table is given below.
Sample |
Sample Proportion |
Probability |
aa |
1 |
1/25 |
ab |
1 |
1/25 |
ac |
0.5 |
1/25 |
ad |
0.5 |
1/25 |
ae |
0.5 |
1/25 |
ba |
1 |
1/25 |
bb |
1 |
1/25 |