题目

Problem

Components are manufactured such that their length in mm is normally distributed with mean $\mu$ and variance $\sigma^2$ . Below is a 95% confidence interval for $\mu$ calculated from a random sample of components.

(11.52,\ 13.75)

Using the same random sample,

(a) find a 90% confidence interval for $\mu$ .

(6)

Four 90% confidence intervals are found from independent random samples.

(b) Calculate the probability that only 3 of these 4 intervals will contain $\mu$ .

(2)

题目中文翻译

元件的长度（单位 mm）服从均值为 $\mu$ 、方差为 $\sigma^2$ 的正态分布。下面是根据一个元件样本算出的 $\mu$ 的 95% 置信区间。

(11.52,\ 13.75)

使用同一个样本，

(a) 求 $\mu$ 的 90% 置信区间。

(b) 从相互独立的 4 个随机样本中得到 4 个 90% 置信区间。求其中恰好只有 3 个区间包含 $\mu$ 的概率。

IAL 2021 June S3 Q3

题目

解答