题目
Spany sells seeds and claims that 5% of its pansy seeds do not germinate. A packet of pansy seeds contains 20 seeds. Each seed germinates independently of the other seeds.
(a) Find the probability that in a packet of Spany’s pansy seeds
(i) more than 2 but fewer than 5 seeds do not germinate,
(ii) more than 18 seeds germinate.
Jem buys 5 packets of Spany’s pansy seeds.
(b) Calculate the probability that all of these packets contain more than 18 seeds that germinate.
Jem believes that Spany’s claim is incorrect. She believes that the percentage of pansy seeds that do not germinate is greater than 5%
(c) Write down the hypotheses for a suitable test to examine Jem’s belief.
Jem planted all of the 100 seeds she bought from Spany and found that 8 did not germinate.
(d) Using a suitable approximation, carry out the test using a 5% level of significance.
(Total for Question 1 is 14 marks)
题目中文翻译
Spany 销售种子，并声称其三色堇种子中有 5% 不发芽。每包三色堇种子有 20 粒，并且每粒种子是否发芽相互独立。
(a) 求在一包 Spany 的三色堇种子中：
(i) 不发芽的粒数多于 2 但少于 5 的概率；
(ii) 发芽的粒数多于 18 的概率。
Jem 买了 5 包 Spany 的三色堇种子。
(b) 计算这 5 包种子都含有多于 18 粒发芽种子的概率。
Jem 认为 Spany 的说法不正确，她认为不发芽的三色堇种子百分比大于 5%。
(c) 写下一个合适检验所需的假设。
Jem 把她从 Spany 买来的 100 粒种子全部种下，发现有 8 粒没有发芽。
(d) 使用适当的近似，在 5% 显著性水平下进行检验。
（第 1 题共 14 分）