题目
Assam produces bags of flour. The stated weight printed on the bags of flour is 3 kg.
The weights of the bags of flour are normally distributed with standard deviation 0.015 kg.
Assam weighs a random sample of 9 bags of flour and finds their mean weight is 2.977 kg.
(a) Calculate the 99% confidence interval for the mean weight of a bag of flour. Give your limits to 3 decimal places.
Assam decides to increase the amount of flour put into the bags.
(b) Explain why the confidence interval has led Assam to take this action.
After the increase a random sample of n bags of flour is taken. The sample mean weight of these n bags is 2.995 kg. A 95% confidence interval for gave a lower limit of less than 2.991 kg.
(c) Find the maximum value of n.
题目中文翻译
Assam 生产面粉袋。袋上印的标称重量是 3 kg。
这些面粉袋的重量服从正态分布，标准差为 0.015 kg。
Assam 随机抽取 9 袋面粉，发现样本均值为 2.977 kg。
(a) 求面粉袋平均重量的 99% 置信区间。答案保留 3 位小数。
Assam 决定增加每袋面粉的装量。
(b) 解释为什么这个置信区间促使 Assam 做出这个决定。
增加后又随机抽取 n 袋面粉，样本均值为 2.995 kg。参数 的 95% 置信区间给出的下限小于 2.991 kg。
(c) 求 n 的最大值。