题目
A manager is reviewing the performance of the staff working for him.
There is a probability of 0.15 that a member of staff performs well.
A random sample of 15 members of staff is taken.
(a) Find the probability that fewer than 2 perform well.
(b) Write down the parameters that should be used to approximate this distribution, justifying your answer.
(c) Using a suitable approximation, find the probability that from a random sample of 300 members of staff no fewer than 50 perform well.
The manager then considers a random sample of 200 members of staff.
Using your answer to part (b), or otherwise, find, when appropriate, the probability that the number of members of staff who perform well in this sample will be within 2 standard deviations of the mean.
(Total for Question 7 is 10 marks)
题目中文翻译
一位经理正在评估其下属员工的表现。
员工表现优秀的概率为 0.15。
随机抽取了 15 名员工样本。
(a) 求少于 2 人表现优秀的概率。
(b) 写出用于近似此分布的参数，并证明你的答案。
(c) 使用适当的近似方法，求在随机抽取的 300 名员工中不少于 50 人表现优秀的概率。
经理随后考虑随机抽取 200 名员工。
使用你在 (b) 中的答案，或以其他方式，在适当时求此样本中表现优秀的员工人数在均值 2 个标准差范围内的概率。
（第 7 题共 10 分）