Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at selects every th that comes off the assembly line starting with the until she obtains a sample of .

Complete question is;

Identify the type of sampling used: random, systematic, convenience, stratified, or cluster.

To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans

Systematic Sample

Step-by-step explanation:

We are told that the quality control manager selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans.

Thus, the selection is from a large sample of produce.

This is synonymous with systematic sample because systematic sample can be defined as a type of probability sampling in which sample members from a larger population are selected according to a random starting point but with a set periodic interval.

This resonates with the statement in the question about selecting every 18th soup from the production assembly line.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18