题目
A golf club has 360 members. The captain of the golf club needs to select 20 players from the club to play in a charity tournament.
The captain decides to use systematic sampling to select the 20 players.
(a) Give a reason for using systematic sampling in this case.
The members are numbered from 001 to 360 and the 5th member on the list is randomly selected as the first player and then every xth member thereafter is selected.
(b) Write down the value of x.
(c) Write down the probability that the sample includes both the 5th and the 6th member on the list.
题目中文翻译
一家高尔夫俱乐部有 360 名会员。队长需要从俱乐部中选出 20 名球员参加一项慈善比赛。
队长决定使用系统抽样来选出这 20 名球员。
(a) 说明在这种情况下使用系统抽样的一个理由。
会员被编号为 001 到 360，第 5 位会员被随机选为第一名球员，然后每隔 x 位会员选取一次。
(b) 写出 x 的值。
(c) 写出样本同时包含第 5 位和第 6 位会员的概率。
解答
(a)
解法一
思路
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这里使用系统抽样并随机决定起点，可以避免队长按球员能力或个人偏好挑选，从而减少选择中的偏差或偏袒。
答题过程
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Systematic sampling reduces the risk of bias or favouritism when the players are selected.
(b)
解法一
思路
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系统抽样的间隔等于总体人数除以样本人数。
答题过程
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(c)
解法一
思路
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从第 5 位开始，每次向后间隔 18 位，样本编号为 ，所以相邻的第 6 位绝不可能同时入选。
答题过程
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The selected members have numbers
so the 6th member cannot be selected with the 5th member. Therefore, the required probability is