题目
Problem
Cars stop at a service station randomly at a rate of 3 every 5 minutes.
(a) Calculate the probability that in a randomly selected 10 minute period,
(i) exactly 7 cars will stop at the service station,
(ii) more than 7 cars will stop at the service station.
(4)
Using a normal approximation, the probability that more than 40 cars will stop at the service station during a randomly selected minute period is 0.2266 correct to 4 significant figures.
(b) Find the value of . You must show all stages of your working.
(9)
(Total for Question 5 is 13 marks)
题目中文翻译
汽车以每 5 分钟 3 辆的随机速率停在服务站。
(a) 计算在随机选择的 10 分钟内
(i) 恰好有 7 辆汽车停在服务站的概率，
(ii) 超过 7 辆汽车停在服务站的概率。
使用正态近似，在随机选择的 分钟内超过 40 辆汽车停在服务站的概率为 0.2266（精确到 4 位有效数字）。
(b) 求 的值。你必须展示所有计算步骤。
（第 5 题共 13 分）