The bakery makes cookies, with a average weight of 30g and a variance of (2.3g)² = 5.29 g². He packs them in either small (20 cookie) or large (30 cookies) packages.

1. Determine the distribution of the sum of the weights (S) of the cookies in the small package. What is the probability that S>615g?
2. What is the probability that, 3 small packages have a weight of at least 25g more than 2 large packages?
3. On the larger package the bakery has stamped "net weight 900g). Legality requires that at least 90% of the packages have to be above this to be able to make this claim. How many of the bakery's packages meet this criteria?
4. What should the average weight of the cookie, so that the criteria is met. (Assuming that the variation in the weight remains unchanged)

The bakery has decided to start marketing his products with fliers. Which follow a N(1.95g, 0.05²)-Distribution, and he packs them in piles of 100.

1. What is the probability that a flier picked from the package, is between the 1.8 g and 2.1 g?
2. Specify a 95% "confidence interval" for the weight of a flier package.
3. What is the probability that the weight of no more than one flier in the entire flier package, is below the expected value of a weight of a single flier?
4. What is the probability that the fliers in the packages have an average weight of more than 1.97g?