题目
Applicants for a pilot training programme with a passenger airline are screened for colour blindness. Past records show that the proportion of applicants identified as colour blind is 0.045
(a) Write down a suitable model for the distribution of the number of applicants identified as colour blind from a total of applicants.
(b) State one assumption necessary for this distribution to be a suitable model of this situation.
(c) Using a suitable approximation, find the probability that exactly 5 out of 120 applicants are identified as colour blind.
(d) Explain why the approximation that you used in part (c) is appropriate.
Jaymini claims that 75% of all applicants for this training programme go on to become pilots.
From a random sample of 96 applicants for this training programme 67 go on to become pilots.
(e) Using a suitable approximation, test Jaymini’s claim at the 5% level of significance. State your hypotheses clearly.
(Total for Question 5 is 14 marks)
题目中文翻译
一项面向客运航空公司的飞行员培训项目会筛查申请者的色盲情况。以往记录显示，被识别为色盲的申请者比例为 0.045。
(a) 写出一个合适的模型，用于表示在总共 名申请者中，被识别为色盲的人数分布。
(b) 说明使该分布适合此情境的一个必要假设。
(c) 使用适当的近似方法，求在 120 名申请者中恰好 5 人被识别为色盲的概率。
(d) 解释为什么 (c) 中使用的近似是适当的。
Jaymini 声称该培训项目的所有申请者中有 75% 最终会成为飞行员。
从该培训项目的 96 名申请者随机抽样，其中 67 人最终成为飞行员。
(e) 使用适当的近似方法，在 5% 显著性水平下检验 Jaymini 的主张。 清楚陈述你的假设。
（第 5 题共 14 分）