题目

Problem

A baker produces bread buns and bread rolls. The weights of buns, $B$ grams, and the weights of rolls, $R$ grams, are such that $B \sim N(55, 1.3^2)$ and $R \sim N(51, 1.2^2)$ .

A bun and a roll are selected at random.

(a) Find the probability that the bun weighs less than 110% of the weight of the roll.

(5)

Two buns are chosen at random.

(b) Find the probability that their weights differ by more than 1 gram.

(6)

The baker sells bread in bags. Each bag contains either 10 buns or 11 rolls. The weight of an empty bag, $S$ grams, is such that $S \sim N(3, 0.2^2)$

(6)

题目中文翻译

一位面包师生产面包小圆包和面包卷。小圆包的重量 $B$ 克和面包卷的重量 $R$ 克分别服从 $B \sim N(55, 1.3^2)$ 和 $R \sim N(51, 1.2^2)$ 。

随机选取一个小圆包和一个面包卷。

(a) 求小圆包的重量小于面包卷重量的 110% 的概率。

随机选取两个小圆包。

(b) 求它们重量相差超过 1 克的概率。

这位面包师把面包装袋出售。每袋要么装 10 个小圆包，要么装 11 个面包卷。空袋重量 $S$ 克，且 $S \sim N(3, 0.2^2)$ 。

IAL 2021 June S3 Q6

题目

解答