Assume you build a candy castle for which you buy a bag of gummy bears, a block of chocolate and a bag of nuts. the weight of the three ingredients is a random variable (x1, x2 and x3) with mean weights μ1 = 200 gram, μ2 = 400 gram and μ3 = 150 gram. the bags and blocks are not measured top perfection so the standard deviation of the three is σ1 = 10, σ2 = 8 and σ3 = 15. the weight of the three ingredients is normally distributed!
a) define the distribution of the weight of the candy castle!

b) what is the chance that the castle will weigh more than 700 gram?

c) what is the chance the castle will weigh between 730 and 755 gram?

d) with 75% chance the castle will weigh between and (symmetric range, as always)

e) the castle weighs more than how much with 95% chance?