Question

Ace Manufacturing Company produces 3,500 screws per day. A check of 100 randomly chosen screws reveals that 4 of them have incorrect lengths, 5 have incorrect diameters, and 3 have both incorrect lengths and diameters.

How many of the screws produced over 2 days should the company predict have only incorrect lengths?

Answer 1

Answer: 70

Explanation:

In one day, the company produced screws = 3,500

⇒ In two days, the company produced screws = 2 × 3,500 = 7,000

Since, In out of 100 randomly chosen screws reveals that 4 of them have incorrect lengths, 5 have incorrect diameters, and 3 have both incorrect lengths and diameters.

Thus, we can write, the percentage of incorrect length = 4%

And, the percentage of incorrect diameter = 5%

Also, the percentage of both incorrect lengths and diameters = 3%

⇒ The percentage that only length is incorrect = the percentage of incorrect length - the percentage of both incorrect lengths and diameters = 4% - 3% = 1%

That is, out of total screws 1 % of screws has only incorrect length,

⇒ Out of 7000 screws the number of screws that has only incorrect length = 1% of 7000 = 70

Thus, In 2 days the predicted number of screws that has incorrect length only = 70