题目
Problem
The number of particles per millilitre in a solution is modelled by a Poisson distribution with mean 0.15
A randomly selected 50 millilitre sample of the solution is taken.
(a) Find the probability that
(i) exactly 10 particles are found,
(ii) between 6 and 11 particles (inclusive) are found.
(4)
Petra takes 12 independent samples of millilitres of the solution. The probability that at least 2 of these samples contain no particles is 0.1184
(b) Using the Statistical Tables provided, find the value of
(6)
(Total for Question 5 is 10 marks)
题目中文翻译
溶液中每毫升的粒子数服从均值为 0.15 的泊松分布。
随机取 50 毫升的溶液样本。
(a) 求以下概率：
(i) 恰好有 10 个粒子，
(ii) 发现 6 到 11 个粒子（含端点）。
Petra 取了 12 个互相独立的 毫升溶液样本。 其中至少 2 个样本不含粒子的概率为 0.1184。
(b) 使用给定的统计表，求 的值。
（第 5 题共 10 分）