The gaskets are only thrown out if they are not within 0.06 pounds of the mean weight of the batch. The first thing we need to do is calculate the mean weight of the batch so that we can know our central point of comparison.
The mean weight of the batch is 0.6 pounds. We need the individual gasket weights w to be less than 0.06 pounds away from 0.6. We can solve for this range of values by writing an absolute value inequality.
|w-0.6|<0.06Since we need the distance from 0.6 to be less than 0.06, we will need to write an andcompound inequality.
w-0.6<0.06 and w-0.6>-0.06
We can solve these cases separately and then combine the results. We will begin with the first case.
With this information we can write the solution set for this compound inequality.
w<0.66 and w>0.54
The acceptable range of weights for the gaskets are those that are less than 0.66 pounds and greater than 0.54 pounds. Therefore, the gasket that needs to be thrown out is the one weighing 0.53 pounds.
