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# Statistics Question- Sampling Distribution of Proportion?

After constructing a new manufacturing machine, 5 prototype integrated circuit chips are produced and it is found that 2 are defective (D) and 3 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?

### 1 Answer

- MLv 79 years agoFavorite Answer
a. ANSWER: Defective Proportion = 40% [2/4]

b. ANSWER; Mean [Expected Value] = 10 [0.40 * 25]

c. ANSWER: No; the Mean from the sampling distribution isn't the same as the proportion. Yes; the sampling proportion always equals the population proportion due to the Central Limit Theorem

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