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

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

It's 100

Because You multiply the sample proportion to 2000

Answer 2

Answer:

Option b is the correct answer.

b)   100 pieces must be defective.

Step-by-step explanation:

The table shows the data of the number of days the 40 units of item would last,

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

Also,  If the product has a lifespan of less than 26 days, it is considered defective.

So, the number of items which are defective out of 40 items are: 2

Hence, the proportion of items that are defective out of 40 items are:

2/40=1/20

Hence, the number of defective items out of 2000 items are:

$=\dfrac{1}{20}\times 2000\\\\=100$

Hence, number of defective items out of 2000 are: 100

Hence, option a), c) and e) are  incorrect.

Also, the population proportion of defective items is:

1/20

and sample proportion is:

40/2000=1/50

as both are not equal.

Hence option d) is incorrect.