在 Urberia，男性的体重以千克为单位，服从分布 $\mathrm{N}(70.3,5.9^2)$。Urberia 的某座人行桥的最大安全荷载为 $1500\,\mathrm{kg}$。当 $n$ 名男子站在桥上时，桥不安全的概率小于 $0.01$。

写出一个必要的假设，并求 $n$ 的最大值。

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。

假设桥上的人可视为总体中的独立随机样本。总质量正态，方差随人数线性增长。把危险概率限制转成正态分位数不等式，再令 $t=\sqrt n$ 解二次不等式。

Assume that the men on the bridge form an independent random sample from the stated population. Let $M$ be their total mass. Then

The bridge is unsafe when $M>1500$. The requirement $\mathrm P(M>1500)<0.01$ implies

Putting $t=\sqrt n>0$ gives

The positive boundary root is

The other root is negative, so for $t>0$ the inequality requires $t<4.52264$, or $n<20.4543\ldots$. The greatest integer satisfying this is

For confirmation, at $n=20$ the unsafe probability is about $0.000184<0.01$, whereas at $n=21$ it is about $0.190>0.01$.