题目
The number of toasters sold by a shop each week may be modelled by a Poisson distribution with mean 4.
A random sample of 35 weeks is taken and the mean number of toasters sold per week is found.
(a) Write down the approximate distribution for the mean number of toasters sold per week from a random sample of 35 weeks.
The number of kettles sold by the shop each week may be modelled by a Poisson distribution with mean .
A random sample of 40 weeks is taken and the mean number of kettles sold per week is found. The width of the 99% confidence interval for is 2.6.
(b) Find an estimate for .
A second, independent random sample of 40 weeks is taken and a second 99% confidence interval for is found.
(c) Find the probability that only one of these two confidence intervals contains .
题目中文翻译
一家商店每周售出的烤面包机数量可以用均值为 4 的泊松分布来建模。
抽取 35 周的随机样本，并求每周售出烤面包机数量的样本均值。
(a) 写出从 35 周随机样本得到的每周售出烤面包机数量均值的近似分布。
该商店每周售出的水壶数量可以用均值为 的泊松分布来建模。
抽取 40 周的随机样本，并求每周售出水壶数量的样本均值。 的 99% 置信区间宽度为 2.6。
(b) 求 的一个估计值。
再抽取第二个彼此独立的 40 周随机样本，并得到 的第二个 99% 置信区间。
(c) 求恰好只有这两个置信区间中的一个包含 的概率。