Question

MULTIPLE CHOICE !! HELP
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.

Answer 1

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

Answer 2

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 3

I would say a

Answer 4

for this reason I think according to the table there is only 5 defective pieces. I might be wrong though.

Answer 5

but theres only 5 wrong in 40 units. its asking how many would be defective out of 2000. @blakeman ..

Answer 6

With 40 samples, take the mean and standard deviation and assume a normal distribution approximation. Calculate the
z-score = (26-mean)/(standard deviation)
and find what % of a normal distribution this corresponds to.

Apply that percentage to 2000 units for that day to estimate the number defective.

Answer 7

you lost me there... too muchh math .. @douglaswinslowcooper

Answer 8

hes right!!!

Answer 9

i know but i dont know how to do all that ..
@blakeman @douglaswinslowcooper

Answer 10

Well, count the number of defectives in the sample of 40 they gave you and use that fraction of 40 to predict that a similar fraction of 2000 will be defective.

If you found 4/40=10% predict 20/2000=10%.

Answer 11

my guess would be that there are about 250 pieces defective.

Answer 12

How many in the sample of 40 had lifetimes less than 26?

Answer 13

2, but 3 had 26.

Answer 14

so 5 ?
@douglaswinslowcooper

Answer 15

defective = "lifespan less than 26 days," so use 2/40 thus 100/2000.

Unfortunately "must" is not true, but perhaps not used literally here.

Answer 16

thank you !!! @douglaswinslowcooper