题目
Navtej travels to work by train. A train leaves the station every 7 minutes and Navtej’s arrival at the station is independent of when the train is due to leave.
(a) Write down a suitable model for the distribution of the time, T minutes, that he has to wait for a train to leave.
(b) Find the mean and standard deviation of T
During a 10-week period, Navtej travels to work by train on 46 occasions.
(c) Estimate the probability that the mean length of time that he has to wait for a train to leave is between 3.4 and 3.6 minutes.
(d) State a necessary assumption for the calculation in part (c).
题目中文翻译
Navtej 乘火车上班。火车每 7 分钟发出一班，而 Navtej 到站的时间与火车预定出发时间无关。
(a) 写出等待火车出发的时间 T（分钟）的一个合适分布模型。
(b) 求 T 的均值和标准差。
在 10 周期间，Navtej 共乘火车上班 46 次。
(c) 估计他等待火车出发的平均时间介于 3.4 到 3.6 分钟之间的概率。
(d) 写出 (c) 小题计算所需的一个必要假设。