题目
A receptionist receives incoming telephone calls and should connect them to the appropriate department. The probability of them being connected to the wrong department on the first attempt is 0.05
A random sample of 8 calls is taken.
(a) Find the probability that at least 2 of these calls are connected to the wrong department on the first attempt.
The receptionist receives 1000 calls each day.
(b) Use a Poisson approximation to find the probability that exactly 45 callers are connected to the wrong department on the first attempt in a day.
The total time, T seconds, taken for a call to be answered by a department has a continuous uniform distribution over the interval [10, 50]
(c) Find P(T > 16)
The number of calls the receptionist receives in a one-minute interval is modelled by a Poisson distribution with mean 6
The receptionist receives a call from Jia and tries to connect it to the right department.
(d) Find the probability that in the next 40 seconds Jia’s call is answered by the right department on the first attempt and the receptionist has received no other calls.
(Total for Question 5 is 12 marks)
题目中文翻译
一名接待员接收来电并应将其连接到适当的部门。第一次尝试时连接到错误部门的概率为 0.05
随机抽取 8 通电话作为样本。
(a) 求其中至少 2 通电话在第一次尝试时被连接到错误部门的概率。
该接待员每天接收 1000 通电话。
(b) 使用泊松近似求一天中恰好有 45 位来电者在第一次尝试时被连接到错误部门的概率。
一通电话被部门接听所需的总时间 T（秒）在区间 [10, 50] 上服从连续均匀分布。
(c) 求 P(T > 16)
该接待员在一分钟间隔内接收的来电数量用均值为 6 的泊松分布建模。
该接待员接到佳的来电并尝试将其连接到正确的部门。
(d) 求在接下来 40 秒内，佳的来电在第一次尝试时被正确部门接听且接待员没有收到其他来电的概率。
（第 5 题共 12 分）