Probability that the mean of multiple measurement is greater than X?

Question

I'm working on the following problem for my stats class:

1. The measurement of atmospheric ozone concentration (in µg/m3) is modeled by a random variable X with distribution N (m, σ2) with σ2 = 3.1.
2. Write the statistical model.
3. In many applications, data are often modeled with the Normal distribution, while often the observed values are by definition positive (e.g. weight, size, speed, duration). Can you explain why?
4. Some day, we make some measurements and we assume that this day the ozone concentration is 178µg/m3 (yet the experimenter doesn’t know this concentration otherwise he wouldn’t need measurements). (a) Compute the probability that a unique measurement is greater than 180? (b) What is the probability that the mean of three measurements is greater than 180 ? (c) How many measurements are necessary for the probability that the mean of these measurements is greater than 180 being less than 1%.

I've already done all exercises up to 4b, where Im stuck.

I did 4a by computing a Z score and doing 1 - P(X<180) = 12.71%

For 4b, how would you guys go about this? should I just do 12.71%^3?

EDIT: changed questions' numbers.