题目
The weights of bags of carrots, C kg, are such that C ~ N(1.2, 0.03^2) Three bags of carrots are selected at random.
(a) Calculate the probability that their total weight is more than 3.5 kg.
The weights of bags of potatoes, R kg, are such that R ~ N(2.3, 0.03^2) Two bags of potatoes are selected at random.
(b) Calculate the probability that the difference in their weights is more than 0.05 kg.
The weights of trays, T kg, are such that T ~ N(2.5, \sqrt{0.1^2})
The random variable G represents the total weight, in kg, of a single tray packed with 10 bags of potatoes where G and T are independent.
(c) Calculate P(G < 2T + 20)
题目中文翻译
胡萝卜袋的重量 C kg 服从分布 C ~ N(1.2, 0.03^2)。 随机抽取 3 袋胡萝卜。
(a) 计算它们总重量大于 3.5 kg 的概率。
土豆袋的重量 R kg 服从分布 R ~ N(2.3, 0.03^2)。 随机抽取 2 袋土豆。
(b) 计算它们重量差大于 0.05 kg 的概率。
托盘的重量 T kg 服从分布 T ~ N(2.5, \sqrt{0.1^2})。
随机变量 G 表示一个装有 10 袋土豆的托盘的总重量（单位 kg），且 G 与 T 相互独立。
(c) 计算 P(G < 2T + 20)。