一家工厂生产某种电子元件。已知所生产的元件中有 15% 存在故障。随机抽取 200 个元件作为样本。

用近似方法求这些元件中超过 40 个存在故障的概率。

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。

故障数服从二项分布，正态近似的均值30、方差25.5；超过40修正40.5。

Let $X\sim\mathrm{B}(200,0.15)$. Since $np=30$ and $n(1-p)=170$ are both greater than 5, use $Y\sim\mathrm{N}(30,25.5)$.

With a continuity correction,