Keep a strict probability condition strict at the quantile boundary

On Crabby Island, a kelong rears Hairy Crabs with mass $H\sim N(\mu,\sigma^2)$ kg. Given $P(H<1.5)=P(H>3.5)=0.33$, state μ.1 mark

(i) Show that σ=2.27.2 marks

(ii) For 4 random Hairy Crabs, find the probability that two weigh between 1.5 and 3.5 kg each and the other two exceed 3.5 kg each.3 marks

Flower Crab mass has an independent normal distribution with mean 3.2 kg and standard deviation 1.3 kg. Find the largest a such that the probability the average mass of 2 Hairy and 3 Flower Crabs exceeds a kg is more than 0.6.3 marks