H1 Maths Alevel Normal Distribution

[CJC2011/Q131 Temasek Confectionery makes two types of mooncakes, namely the Snow Skin Durian Mooncake and the Baked Mooncake With Double Yolk, The masses of Snow Skin and Baked Mooncakes can be modelled using two (1) 0.325 normal distributions with means and standard deviations as shown in the following table (#) 0.835 Mean Standard (in) The masses mass Deviation Baked Mooncake Baked Mooncake 90 g 15 g and Snow-skin Snow-Skin Mooncake 55 g 8 g Mooncake follow independent The Snow-Skin Mooncakes are sold by weight at $0. 15 per gram, while normal distributic the Baked Mooncakes are sold by weight at $0.20 per gram. (iv) 15 Find the probability that twice the weight of a randomly chosen Baked Mooncake is less than the total weight of three randomly chosen Snow-Skin Mooncakes. Find the probability that the total cost of 4 randomly chosen Baked Mooncakes and 6 randomly chosen Snow-Skin Mooncakes exceeds $115. State an assumption you have made in your calculations in (ii), A random sample of n Baked Mooncakes is taken. Find the least value of n such that the probability that the sample mean mass is at least 95g is less than 0.1. * ~( 70, 13