题目
Sam is a telephone sales representative. For each call to a customer
• Sam either makes a sale or does not make a sale
• sales are made independently
Past records show that, for each call to a customer, the probability that Sam makes a sale is 0.2
(a) Find the probability that Sam makes
(i) exactly 2 sales in 14 calls,
(ii) more than 3 sales in 25 calls.
Sam makes n calls each day.
(b) Find the minimum value of n
(i) so that the expected number of sales each day is at least 6
(ii) so that the probability of at least 1 sale in a randomly selected day exceeds 0.95
(Total for Question 1 is 10 marks)
题目中文翻译
山姆是一名电话销售代表。对于给客户的每次通话
• 山姆要么成交要么未成交
• 销售是独立进行的
过去的记录显示，对于给客户的每次通话，山姆成交的概率为 0.2
(a) 求山姆在以下情况成交的概率
(i) 在 14 次通话中恰好成交 2 次，
(ii) 在 25 次通话中成交超过3 次。
山姆每天打 n 次电话。
(b) 求最小的 n 值
(i) 使得每天的预期成交数至少为6
(ii) 使得随机选择的一天中至少成交 1 次的概率超过 0.95
（第 1 题共 10 分）