题目
The weights, S kg, of bags of sand are such that S ~ N(18, 0.03^2).
Three bags of sand are selected at random.
(a) Using standardisation, calculate the probability that their total weight is more than 54.1 kg.
The weights, C kg, of bags of cement are such that C ~ N(25, 0.03^2).
Two bags of cement are selected at random.
(b) Using standardisation, calculate the probability that their weights differ by more than 0.02 kg.
The weights, P kg, of pallets are such that P ~ N(15, 0.2^2).
The random variable T represents the total weight, in kg, of 28 bags of sand with 5 bags of cement and a single pallet of weight P1.
(c) Using standardisation, calculate the probability that T < 30P1 + 190.
题目中文翻译
沙袋的重量 S kg 满足 S ~ N(18, 0.03^2)。
随机选取 3 个沙袋。
(a) 用标准化方法求它们总重量大于 54.1 kg 的概率。
水泥袋的重量 C kg 满足 C ~ N(25, 0.03^2)。
随机选取 2 个水泥袋。
(b) 用标准化方法求它们重量相差超过 0.02 kg 的概率。
托盘的重量 P kg 满足 P ~ N(15, 0.2^2)。
随机变量 T 表示 28 个沙袋、5 个水泥袋和 1 个重量为 P1 的托盘的总重量，单位为 kg。
(c) 用标准化方法求 T < 30P1 + 190 的概率。