Maths H1 Alevel Normal distribution

[NJC 2009/Q13 (modified)] 4 = 2.5 On Crabby Island, a fishmonger rears many types of live seafood in his (ii) 0.00292 ; kelong, one of which is a particular type of crab named the Hairy Crab. The a = 2.72 kg weight H, in kg, of a random Hairy Crab follows a normal distribution with mean u kg and standard deviation o kg. Given that P(H 3.5) =0.33, state the value of H . Show that o = 2.27. Find the probability that out of 100 Hairy Crabs, at least 80 will weigh more than 1.5 kg. Another type of crab named Flower Crab found on Crabby Island follows an independent normal distribution with mean weight 3.2 kg and standard deviation 1.3 kg. Find the value of a such that the probability of the average weight of two randomly chosen Hairy Crabs and three randomly chosen Flower Crabs exceeds a kg is 0.6