The reason you cant get an answer is because it depends on which programs you are applying to. If you apply to the top 20 programs in the country and not a single middle tier program, then 20 is not enough. If you apply to 5-10 top 20's, another 5-10 middle tier academic institutes, and a few safety programs then you could easily be covered by 15 applications (if you rank 10 programs and a handful of middle or safety tier as a average to strong applicant you are likely in good shape).
Keep in mind psych has gotten a lot more competitive recently, so I presume you mean average/strong compared to the current competition.