题目
An optician is testing patients for a specific eye condition.
It is known from past records that 5% of patients have this eye condition.
(a) Find the probability that from a random sample of 30 patients
(i) exactly one patient has the eye condition,
(ii) no more than 2 patients have the eye condition.
The optician claims that the proportion of patients with the eye condition has changed.
A random sample of 150 patients is taken and 13 have the eye condition.
(b) Using a suitable approximation, carry out an appropriate test to investigate the optician’s claim. Use a 5% level of significance and state your hypotheses clearly.
(Total for Question 4 is 8 marks)
题目中文翻译
一位眼科医生正在检测患者是否患有特定眼疾。
根据过去的记录，已知 5% 的患者患有此眼疾。
(a) 求在随机抽取的 30 名患者中
(i) 恰好有一名患者患有此眼疾的概率，
(ii) 不超过 2 名患者患有此眼疾的概率。
眼科医生声称患有此眼疾的患者比例已经改变。
随机抽取了 150 名患者样本，其中 13 人患有此眼疾。
(b) 使用适当的近似方法，进行适当的检验来调查眼科医生的声明。使用 5% 的显著性水平并清楚地陈述你的假设。
（第 4 题共 8 分）