题目
(a) Explain what you understand by the sampling distribution of a statistic.
A factory produces beads in bags for craft shops. A small bag contains 40 beads, a medium bag contains 80 beads and a large bag contains 150 beads. The factory produces small, medium and large bags in the ratio 5:3:2 respectively.
A random sample of 3 bags is taken from the factory.
(b) Find the sampling distribution for the range of the number of beads in the 3 bags in the sample.
A random sample of n sets of 3 bags is taken. The random variable Y represents the number of these n sets of 3 bags that have a range of 70
(c) Calculate the minimum value of n such that P(Y = 0) < 0.2
(Total for Question 6 is 11 marks)
题目中文翻译
(a) 解释你对统计量的抽样分布的理解。
一家工厂为手工店生产袋装珠子。小袋含 40 颗珠子，中袋含 80 颗，大袋含 150 颗。工厂生产小、中、大袋的比例分别为 5:3:2。
随机抽取 3 袋。
(b) 求这 3 袋样本中珠子数量极差的抽样分布。
随机抽取 n 组，每组 3 袋。随机变量 表示这 n 组中极差为 70 的组数。
(c) 求使 的最小 。
（第 6 题共 11 分）