题目
A local pottery makes cups. The number of faulty cups made by the pottery in a week follows a Poisson distribution with a mean of 6 In a randomly chosen week, the probability that there will be at least faulty cups made is 0.1528
(a) Find the value of
(b) Use a normal approximation to find the probability that in 6 randomly chosen weeks the total number of faulty cups made is fewer than 32
A week is called a “poor week” if at least faulty cups are made, where is the value found in part (a).
(c) Find the probability that in 50 randomly chosen weeks, more than 1 is a “poor week”.
(Total for Question 1 is 11 marks)
题目中文翻译
一家本地陶艺坊制作杯子。该陶艺坊每周生产的有瑕疵杯子数量服从均值为 6 的泊松分布。
在随机选取的一周中，至少有 个有瑕疵杯子的概率为 0.1528。
(a) 求 的值。
(b) 使用正态近似，求在随机选取的 6 周内，有瑕疵杯子总数少于 32 的概率。
如果至少有 个有瑕疵杯子，则该周被称为“糟糕的一周”，其中 为 (a) 中求得的值。
(c) 求在随机选取的 50 周中，超过 1 周是“糟糕的一周”的概率。
（第 1 题共 11 分）