题目
Superbounce is a manufacturer of tennis balls. It knows from past records that 10% of its tennis balls fail a bounce test.
(a) Find the probability that from a random sample of 10 of these tennis balls
(i) at least 4 fail the bounce test
(ii) more than 1 but fewer than 5 fail the bounce test.
The managing director makes changes to the production process and claims that these changes will reduce the probability of its tennis balls failing the bounce test.
After the changes were made a random sample of 50 of the tennis balls were tested and it was found that 2 failed the bounce test.
(b) Test, at the 5% significance level, whether or not this result supports the managing director’s claim.
In a second random sample of n tennis balls it was found that none failed the bounce test. As a result of this sample, the managing director’s claim is supported at the 1% significance level.
(c) Find the smallest possible value of n
题目中文翻译
Superbounce 是一家网球制造商。 根据以往记录，它生产的网球有 10% 无法通过弹跳测试。
(a) 求从 10 个这样的网球组成的随机样本中：
(i) 至少 4 个未通过弹跳测试的概率；
(ii) 失败数多于 1 但少于 5 的概率。
(b) 在 5% 显著性水平下检验：这一结果是否支持总经理关于改进生产流程后会降低网球未通过弹跳测试概率的说法。
(c) 在第二个包含 n 个网球的随机样本中，没有一个未通过弹跳测试。 若该样本支持总经理的说法，则 1% 显著性水平下最小的 n 是多少。