First of all:

Let X be the random variable

*weight of pre-packaged 1-lb bags*.

Let Y be the random variable

*sum of the weights of three pre-packaged 1-lb bags*. Then:

Y = X + X + X ~ N(1.18 + 1.18 + 1.18, 0.07^2 + 0.07^2 + 0.07^2) = N(3.54, 0.0147) = N(3.54, 0.12124^2).

Note that 0.12124^2 is the variance.

See the result in

this link.

Let W be the random variable

*weight of pre-packaged 3-lb bags*.

You want to calculate Pr(Y - W > 0). So consider the random variable D = Y - W:

D ~ N(3.54 - 3.22, 0.12124^2 + 0.09^2) = N(0.32, 0.0228) = N(0.32, 0.151^2).

Note that 0.151^ is the variance.

See the result in

this link.

Now calculate Pr(D > 0).

I get 0.983 (correct to three decimal places) as the answer.

Note: I reserve the right for this reply to contain arithmetic errors.