Aim High

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

For the second part you will need to use the formula for the expected value of a random variable $X$:
$$E(X) = \int^\infty_{-\infty} xf(x) dx$$

Don't forget that you can split an integral into two parts
$$\int^\infty_{-\infty} xf(x) dx=\int^a_{-\infty} xf(x) dx+\int^\infty_a xf(x) dx$$

You might also want to use the Erf function in Excel to work out the numbers and to change variables in any integrals to reduce them to standard $N(0,1)$ cases.