题目

Problem

A company produces bricks.

The weight of a brick, $B$ kg, is such that $B \sim N(1.96, 0.003^2)$ .

Two bricks are chosen at random.

(a) Find the probability that the difference in weight of the 2 bricks is greater than 0.1 kg

(5)

A random sample of $n$ bricks is to be taken.

(b) Find the minimum sample size such that the probability of the sample mean being greater than 2 is less than 1%

(5)

The bricks are randomly selected and stacked on pallets.

The weight of an empty pallet, $E$ kg, is such that $E \sim N(21.8, 0.6^2)$ .

The random variable $M$ represents the total weight of a pallet stacked with 500 bricks.

The random variable $T$ represents the total weight of a container of cement.

Given that $T$ is independent of $M$ and that $T \sim N(774, 1.8^2)$

(7)

题目中文翻译

一家公司生产砖块。

砖块重量 $B$ kg 服从 $B \sim N(1.96, 0.003^2)$ 。

随机选取 2 块砖。

(a) 求这 2 块砖重量差大于 0.1 kg 的概率。

随机抽取 n 块砖组成样本。

(b) 求最小样本量，使样本均值大于 2 的概率小于 1%。

砖块被随机选取并堆放在托盘上。

空托盘的重量 $E$ kg 服从 $E \sim N(21.8, 0.6^2)$ 。

随机变量 $M$ 表示装有 500 块砖的托盘总重量。

随机变量 $T$ 表示一箱水泥的总重量。

已知 $T$ 与 $M$ 独立，且 $T \sim N(774, 1.8^2)$ 。

IAL 2021 Oct S3 Q7