题目

Problem

A shop sells rods of nominal length 200 cm. The rods are bought from a manufacturer who uses a machine to cut rods of length $L$ cm, where $L \sim N\left(\mu, \, 0.2^2\right)$

The value of $\mu$ is such that there is only a 5% chance that the rod, selected at random from those supplied to the shop, will have a length less than 200 cm.

(a) Find the value of $\mu$ to one decimal place.

(3)

A customer buys a random sample of 8 of these rods.

(b) Find the probability that at least 3 of these rods will have a length less than 200 cm.

(3)

Another customer buys a random sample of 60 of these rods.

(c) Using a suitable approximation, find the probability that more than 5 of these rods will have length less than 200 cm.

(3)

(Total for Question 1 is 9 marks)

题目中文翻译

一家商店出售标称长度为 200 cm 的 rods。这些 rods 从制造商处购买，制造商使用机器切割长度为 $L$ cm 的 rods，其中 $L \sim N\left(\mu, \, 0.2^2\right)$

$\mu$ 的值使得从商店供应的 rods 中随机选取一根，其长度小于 200 cm 的概率仅为 5%。

(a) 求 $\mu$ 的值，保留一位小数。

一位顾客随机购买了 8 根这样的 rods。

(b) 求其中至少有 3 根 rods 长度小于 200 cm 的概率。

另一位顾客随机购买了 60 根这样的 rods。

（第 1 题共 9 分）

IAL 2026 Jan S2 A Q1

题目

解答