题目
The length of pregnancy for a randomly selected pregnant sheep is D days where
D ~ N(112.4, σ²)
Given that 5% of pregnant sheep have a length of pregnancy of less than 108 days,
(a) find the value of σ
Qiang selects 25 pregnant sheep at random from a large flock.
(b) Find the probability that more than 3 of these pregnant sheep have a length of pregnancy of less than 108 days.
Charlie takes 200 random samples of 25 pregnant sheep.
(c) Use a Poisson approximation to estimate the probability that at least 2 of the samples have more than 3 pregnant sheep with a length of pregnancy of less than 108 days.
(Total for Question 2 is 8 marks)
题目中文翻译
随机选择的一只怀孕母羊的妊娠天数为 D 天，其中
D ~ N(112.4, σ²)
已知 5% 的怀孕母羊的妊娠天数少于 108 天，
(a) 求 σ 的值
强从一大群怀孕母羊中随机选择 25 只。
(b) 求超过 3 只怀孕母羊的妊娠天数少于 108 天的概率。
查理随机抽取 200 个 25 只怀孕母羊的样本。
(c) 使用泊松近似来估计至少有 2 个样本中超过 3 只怀孕母羊的妊娠天数少于 108 天的概率。
（第 2 题共 8 分）