Question

An assembly line is manufacturing gears that have a circumference of 8 cm. The tolerance for the circumference of the gears is 0.03 cm. To check the quality of the gears, the foreman has pulled 19 off the line and measured their circumferences. What percentage of the gears fall outside of the tolerance? Round your answer up to the nearest percentage. {7.96, 7.965, 7.97, 7.982, 7.99, 7.99, 8, 8, 8, 8, 8, 8, 8.01, 8.01, 8.012, 8.02, 8.025, 8.029, 8.031} _____ %

Answer 1

16

Explanation:

Find the number of gears outside the tolerance, then calculate that number as a percentage of the set of 19 gears.

Answer 2

16% (rounded)

Explanation:

8 cm with a tolerance of 0.03 means:

8 - 0.03 = 7.97

and

8 + 0.03 = 8.03

Hence, all should fall between 7.97 and 8.03

Let's check:

7.96 Outside

7.965 Outside

7.97 within

7.982 within

7.99 within

8 within

8.01 within

8.012 within

8.02 within

8.025 within

8.029 within

8.031 Outside

So 3 of them fall outside the tolerance from 19. The percentage is thus:

3/19 * 100 = 15.79%

To the nearest percentage, that's 16%