Shift Output Series Anomaly
A packing line logs cartons completed per 10-minute block across a 7-block shift. The first four blocks read: 48, 43, 39, 36. The supervisor expects the same rule to continue for the remaining three blocks. A second line runs blocks of 60, 55, 51, 48 and must follow an analogous rule. Midway through block 5 the line is briefly paused, and the recorded value for that block is 34 instead of the value the pattern predicts. The shift report requires the full corrected sequence, the total output for the 7 blocks, and a flag on whether the pause distorted the total by more than 5 percent.
1. Determine the rule governing the first line, state the corrected 7-block sequence, and give the total output.
Read the worked answer
Differences: 48→43 (−5), 43→39 (−4), 39→36 (−3). The decrement grows by 1 each block, so the next differences are −2, −1, 0.
Corrected sequence: 48, 43, 39, 36, 34, 33, 33.
Note block 5 already equals 34, so the pause did not change the value.
Total = 48+43+39+36+34+33+33 = 266.
2. The second line follows an analogous rule. Confirm its next three terms and compare the two lines' totals.
Read the worked answer
Second line differences: 60→55 (−5), 55→51 (−4), 51→48 (−3). Same rule: −2, −1, 0.
Next terms: 48−2=46, 46−1=45, 45−0=45.
Sequence: 60, 55, 51, 48, 46, 45, 45. Total = 60+55+51+48+46+45+45 = 350.
Line 2 total exceeds Line 1 by 350 − 266 = 84 cartons.
3. If block 5 had instead been recorded as 30, would the total be distorted by more than 5 percent of the corrected total?
Read the worked answer
Corrected total is 266. A record of 30 instead of 34 lowers the total by 4, giving 262.
Distortion = 4 / 266 ≈ 0.01504, i.e. about 1.5 percent.
That is well under the 5 percent threshold (5 percent of 266 = 13.3 cartons), so the flag would be no.