Discussion questions · Section 3 of 3

$X\sim N(3,4)$, with mean 3 and variance 4. S sums 100 independent observations of X; T sums a further 300 independent observations. Give numerical answers to 3 decimal places.

(i) Find $P(S>310)$.

(ii) Find $P(3S>50+T)$.

(iii) N sums n independent observations of X. State the approximate value of $P(N>3.5n)$ as n becomes very large, with justification.