Question

A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it could last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected.

39 31 38 40 29
32 33 39 35 32
32 27 30 31 27
30 29 34 36 25
30 32 38 35 40
29 32 31 26 26
32 26 30 40 32
39 37 25 29 34

8
Select the correct answer.
Which statement is true about the population proportion of defective pieces in the 2,000 items?
A.
5 pieces must be defective.
B.
100 pieces must be defective.
C.
More than 100 pieces must be defective.
D.
The population proportion of defective pieces must be equal to the sample proportion.
E.
There is insufficient data to calculate the proportion of defective pieces.

Answer 1

B. 100 pieces must be defective.

Explanation:

Let's calculate a projection of how many defective products we should have in a production of 2,000 units a day, based on the quality sample of 40 units provided.

So, we have 40 units sampled, out of those 40, 2 units are defective.

We'll assume the sampling is representative of the overall quality of the production.

How much bigger is the daily production (2,000) compared to the sampling (40)? 2,000 / 40 = 50.

So, the production is 50 times larger than the sample.

Since we found 2 defective units in the sampling, we could assume 100 (2 x 50) defective units in the daily production of 2,000.

Although I would replace "must" by "should" in the wording of the answer, because we cannot be sure it will be exactly 100, could be 97 or 101.