题目
A market stall sells vegetables. Two of the vegetables sold are broccoli heads and cabbages.
The weights of these broccoli heads, B kilograms, follow a normal distribution
The weights of these cabbages, C kilograms, follow a normal distribution
(a) Find the probability that the total weight of two randomly chosen broccoli heads is less than the weight of a randomly chosen cabbage.
Broccoli heads cost £2.50 per kg and cabbages cost £3.00 per kg.
Jaymini buys 1 broccoli head and 2 cabbages, chosen randomly.
(b) Find the probability that she pays more than £7
The market stall offers a discount for buying 5 or more broccoli heads. The price with the discount is £w per kg.
Let £D be the price with the discount of 5 broccoli heads.
(c) Find, in terms of w, the mean and standard deviation of D
Given that P(D < 6) < 0.1
(d) find the smallest possible value of w, giving your answer to 2 decimal places.
题目中文翻译
一个菜摊出售蔬菜。其中两种蔬菜分别是西兰花和卷心菜。
这些西兰花的重量 B（单位：千克）服从正态分布
这些卷心菜的重量 C（单位：千克）服从正态分布
(a) 求两颗随机选取的西兰花总重量小于一颗随机选取的卷心菜重量的概率。
(b) 西兰花每千克 £2.50，卷心菜每千克 £3.00。
Jaymini 随机购买 1 颗西兰花和 2 颗卷心菜。
求她支付超过 £7 的概率。
(c) 以 w 英镑每千克出售 5 颗或以上西兰花时可享受折扣。 设 £D 为 5 颗西兰花的折扣价格。
求 D 的均值和标准差，用 w 表示。
(d) 已知 P(D < 6) < 0.1，求 w 的最小可能值，答案保留 2 位小数。