Final answer:
To identify the cup that is not within the specified tolerance, calculate the upper and lower limits of the tolerance and compare them to the actual diameter of each cup in the sample. The fourth cup with a diameter of 5.5in is not within the specified tolerance.
Step-by-step explanation:
In this question, we are given the tolerance for the diameter of the cup's mouth, which is 5in ± 8%. We have a sample of cups with their diameters listed in a table. To identify the cup that is not within the specified tolerance, we need to calculate the upper and lower limits of the tolerance and compare them to the actual diameter of each cup in the sample.
To calculate the upper limit, we add 8% of 5in to the nominal value of 5in. This gives us 5in + 0.08 * 5in = 5in + 0.4in = 5.4in. To calculate the lower limit, we subtract 8% of 5in from the nominal value of 5in. This gives us 5in - 0.08 * 5in = 5in - 0.4in = 4.6in. Now, we compare the actual diameters of the cups in the sample to these upper and lower limits to determine which cup is not within the specified tolerance.
Looking at the table of cup diameters, we can see that the fourth cup has a diameter of 5.5in, which is greater than the upper limit of 5.4in. Therefore, the fourth cup is not within the specified tolerance.