题目
The number of cars entering a safari park per 10-minute period can be modelled by a Poisson distribution with mean 6
(a) Find the probability that in a given 10-minute period exactly 8 cars will enter the safari park.
(b) Find the smallest value of n such that the probability that at least n cars enter the safari park in 10 minutes is less than 0.05
The probability that no cars enter the safari park in m minutes, where m is an integer, is less than 0.05
(c) Find the smallest value of m
A car enters the safari park.
(d) Find the probability that there is less than 5 minutes before the next car enters the safari park.
Given that exactly 15 cars entered the safari park in a 30-minute period,
(e) find the probability that exactly 1 car entered the safari park in the first 5 minutes of the 30-minute period.
Aston claims that the mean number of cars entering the safari park per 10-minute period is more than 6
He selects a 15-minute period at random in order to test whether there is evidence to support his claim.
(f) Determine the critical region for the test at the 5% level of significance.
(Total for Question 4 is 15 marks)
题目中文翻译
每 10 分钟进入一个野生动物园的汽车数量可用均值为 6 的泊松分布建模。
(a) 求在给定的 10 分钟内恰好有 8 辆车进入的概率。
(b) 求最小的整数 ，使得在 10 分钟内至少有 辆车进入的概率小于 0.05。
在 分钟内没有车进入野生动物园的概率小于 0.05，其中 为整数。
(c) 求最小的 。
一辆车进入了野生动物园。
(d) 求下一辆车进入前少于 5 分钟的概率。
已知在 30 分钟内恰好有 15 辆车进入，
(e) 求在这 30 分钟的前 5 分钟内恰好有 1 辆车进入的概率。
Aston 声称每 10 分钟进入野生动物园的汽车平均数大于 6。
他随机选取一个 15 分钟的时间段，以检验是否有证据支持他的说法。
(f) 求 5% 显著性水平下的临界域。
（第 4 题共 15 分）