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 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

Answer:

15.8 %

Step-by-step explanation:

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

7.96, 7.965, 8.031 falls out side the tolerance

=> (3/19) * 100  = 15.8 %

for Entire Batch

Mean =  8 + (-0.04 -0.335 - 0.03 - 0.018 -0.01 - 0.01 + 0+ 0+ 0 + 0 + 0.01 + .012 +.02 + .025 + .029 + .031)/19

Then Find Standard Deviation

Then Find z values using  ( x - Mean)/ SD

x = 7.97  & 8.03

Then from that gears falling outside of the tolerance can be calculated