Maroulla 的计算器能够生成介于 $0.000$ 与 $0.999$ 之间（含端点）、保留 $3$ 位有效数字的随机数。她计划用计算器从健身俱乐部的 $851$ 名会员中抽取一个样本。她把会员从 $1$ 到 $851$ 编号，然后用计算器生成若干随机数。她将每个随机数乘以 $851$，再向上取到下一个整数，得到样本中一名会员的编号。这个编号称为“会员编号”。

(a) Maroulla 生成的第一个随机数是 $0.401$。

求这个随机数产生的会员编号。

(b) 求能产生下列会员编号的所有可能随机数，保留 $3$ 位小数。

(i) 会员编号为 $680$。

(ii) 会员编号为 $850$。

(c) 简要说明为什么你在 (b) 中的答案表明 Maroulla 的方法无法得到随机样本。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

先乘以人数，再向上取整。

Since $851(0.401)=341.251$, rounding up gives member number $\boxed{342}$.

向上取整规则对应左开右闭区间，在其中列出符合精度的输出。

For output $u$ to give member number $680$,

so

This is approximately $0.797885<u\le0.799060$. The possible calculator outputs are $\boxed{0.798,\ 0.799}$.

同样先解取整不等式，再检查三位小数。

For member number $850$,

Thus

The interval is approximately $0.997650<u\le0.998825$, so the only output is $\boxed{0.998}$.

两个成员对应的等可能输出个数不同，因此选择概率不同。

Two outputs select member $680$, but only one selects member $850$. These outputs are equally likely, so member $680$ has twice the selection probability of member $850$. The members do not have equal chances, so the method does not produce a random sample.