Okay, so the problem gives us mean=58 and SD=1.5, normally distributed.
The first 5 parts of the problem ask for various probabilities, which I'm fine with.

The last part of the problem says to find the expected value, E(W^2 + 2W)
I really have no idea how to do this, when I look through my notes, I can't find any mention of expected values in normal distributions (considering they would just be the mean...)

Any help is appreciated, thanks.

Anyone?

What's W? Gaussians are "Linear", which means that any linear combinations of Gaussian RVs will still be Normally distributed.

W is just a variable, in this case it represents WEIGHT, which is what's normally distributed (weight of pizzas in the problem).

So would E(W^2 + 2W) just be the same as E(W), since it's originally Normally Distributed?

No actually. I read your post wrongly but that's not correct even if that was a linear combo

So we know expectation is a linear operator right?

So first split this into

E(W^2) + E(2W)

also by linearity of expectation

=E(W^2) + 2E(W)

now we know that variance is E(W^2) - E(W)^2 right?

so this is the same as


= variance(W) + E(W)^2 + 2E(W)

I'm not familiar with all these "linearity" rules, but it makes sense.
Thanks.