题目
Bhavna produces rolls of cloth. She knows that faults occur randomly in her cloth at a mean rate of 1.5 every 15 metres.
(a) Find the probability that in 15 metres of her cloth there are
(i) less than 3 faults,
(ii) at least 6 faults.
Each roll contains 100 metres of Bhavna’s cloth. She selects 15 rolls at random. (b) Find the probability that exactly 10 of these rolls each have fewer than 13 faults.
Bhavna decides to sell her cloth in pieces. Each piece of her cloth is 4 metres long. The cost to make each piece is £5.00 She sells each piece of her cloth that contains no faults for £7.40 She sells each piece of her cloth that contains faults for £2.00 (c) Find the expected profit that Bhavna will make on each piece of her cloth that she sells.
(Total for Question 1 is 11 marks)
题目中文翻译
Bhavna 生产布卷。她知道布上的瑕疵随机出现，平均速率为每 15 米 1.5 个。
(a) 求在 15 米布中有以下情况的概率：
(i) 少于 3 个瑕疵，
(ii) 至少 6 个瑕疵。
每卷包含 100 米 Bhavna 的布。 她随机选取 15 卷。 (b) 求恰好有 10 卷各自瑕疵少于 13 个的概率。
Bhavna 决定把布切成小段出售。 每段布长 4 米。 每段制作成本为 £5.00。 若一段布没有瑕疵，售价为 £7.40。 若一段布有瑕疵，售价为 £2.00。 (c) 求 Bhavna 每出售一段布所能获得的期望利润。
（第 1 题共 11 分）