Here you have to work with z-score table.
Formula: z=(x-μ)/σ, where x is the # of dogs, μ = mean and σ = standard deviation.
You look up in the score table for which value, z corresponds to 0.84 and you will find that z = 0.7995 for a probability of 84%
0.7995 = (x-18)/3 → x =20.39 or 84% weighs under 20.39 pounds