Suppose the random variables X1,…,Xn+1 follow normal distributions N(μi,σi2), i=1,…,n+1, and their dependence is modelled by Archimedean copula with generator ϕ. Then, the following results are established for the largest order statistics: (1) Suppose tϕ′(t)1−ϕ(t) and Φ−1(ϕ(t))Φ′(Φ−1(ϕ(t)))tϕ′(t) are increasing in t>0, then, if μ1=⋯=μn+1 and σn+1≥σi for i=1,…,n, we have Xn:n≤hrXn+1:n+1; (2) Suppose tϕ′(t)ϕ(t) is decreasing and Φ−1(ϕ(t))Φ′(Φ−1(ϕ(t)))tϕ′(t) is increasing in t>0, then, if μ1=⋯=μn+1 and σn+1≤σi for i=1,…,n, we have Xn:n≤rhXn+1:n+1; (3) Suppose tϕ′(t)1−ϕ(t) and Φ′(Φ−1(ϕ(t)))tϕ′(t) are increasing in t>0, then, if σ1=⋯=σn+1 and μn+1≥μi for i=1,…,n, we have Xn:n≤hrXn+1:n+1; (4) Suppose tϕ′(t)ϕ(t) is decreasing and Φ′(Φ−1(ϕ(t)))tϕ′(t) is increasing in t>0, then, if σ1=⋯=σn+1 and μn+1≤μi for i=1,…,n, we have Xn:n≤rhXn+1:n+1. Analogous results are then established for smallest order statistics as well. In addition, we present some numerical examples to illustrate all the results established here. Finally, some concluding remarks are made.