题目
Problem
Krishi owns a farm on which he keeps chickens.
He selects, at random, 10 of the eggs produced and weighs each of them.
You may assume that these weights are a random sample from a normal distribution with standard deviation 1.9 g
The total weight of these 10 eggs is 537.2 g
(a) Find a 95% confidence interval for the mean weight of the eggs produced by Krishi’s chickens.
(4)
Krishi was hoping to obtain a 99% confidence interval of width at most 1.5 g
(b) Calculate the minimum sample size necessary to achieve this.
(4)
题目中文翻译
Krishi 在自己的农场里养鸡。
他随机选取了产出的 10 枚鸡蛋，并称量每一枚。
你可以假设这些重量是来自一个标准差为 1.9 g 的正态分布的随机样本。
这 10 枚鸡蛋的总重量为 537.2 g。
(a) 求 Krishi 的鸡所产鸡蛋平均重量的 95% 置信区间。
(b) 计算达到“宽度至多为 1.5 g”的 99% 置信区间所需的最小样本量。