Pet peeve warning!

Ah. Better now! Pet peeve over.

You did it right, but your interpretation was wrong. (Note the section in red letters below.) Let me explain in detail:

Okay, my sketch of the Free-Body Diagram has a weight w acting downward, a normal force N acting upward, an applied force F acting horizontally to the right on the box, and a static friction force f acting to the left. I have a +x direction to the right and a +y direction upward.

Applying Newton's 2nd in the y direction we get:

(Sum)Fy = N - w = ma_y = 0 (since the box is not accelerating upward.)

Thus N = w = mg

Applying Newton's 2nd in the x direction we get:

(Sum)Fx = F - f = ma_x = 0 (since the box is not accelerating horizontally.)

I'm going to calculate the maximum force we can apply to the box such that the box will not move. In this case the static friction force will be equal to (mu)N. (It is generally less than or equal to this amount.) Thisshouldbe greater than 120 N if the box is to be stationary.

Thus F = f = (mu)N = (mu)mg = (1/7)*100*9.8 = 140 N.

Since we can apply up to 140 N before the box moves and we are only applying 120 N, the box will be stationary.

-Dan