题目
It is known that a particular variety of tulip produces yellow flowers with a probability of 0.25
A random sample of 15 tulips of this variety is purchased.
(a) Find the probability that more than 4 of these tulips will produce yellow flowers.
(b) Find the least number of tulips that needs to be purchased so that the probability of at least 1 tulip producing yellow flowers exceeds 0.95
Another random sample of 100 tulips of this variety is purchased.
(c) Use a suitable approximation to find the probability that, of these 100 tulips, more than 21 but no more than 30 will produce yellow flowers. Show your working clearly.
(Solutions relying entirely on calculator technology are not acceptable.)
For this particular variety, it is thought that the probability of a tulip producing red flowers is 0.3
A random sample of 25 tulips of this variety was purchased. When these tulips flowered, 10 of them produced red flowers.
(d) Use this random sample of 25 tulips to test whether this variety of tulip has a probability greater than 0.3 of producing red flowers. Use a 10% level of significance and state your hypotheses clearly.
(Total for Question 5 is 15 marks)
题目中文翻译
已知某个郁金香品种以 0.25 的概率开出黄色花朵。
随机购买了 15 株该品种的郁金香。
(a) 求超过 4 株郁金香开出黄色花朵的概率。
(b) 求需要购买的最少郁金香数量，使得至少 1 株开出黄色花朵的概率超过 0.95。
又随机购买了 100 株该品种的郁金香。
(c) 使用适当的近似方法求在这 100 株郁金香中，超过 21 株但不超过 30 株开出黄色花朵的概率。清楚地展示你的计算过程。
对于该品种，认为郁金香开出红色花朵的概率为 0.3。
随机购买了 25 株该品种的郁金香。当这些郁金香开花时，其中 10 株开出了红色花朵。
(d) 使用此 25 株郁金香的随机样本来检验该品种开出红色花朵的概率是否大于 0.3。使用 10% 的显著性水平并清楚地陈述你的假设。
（第 5 题共 15 分）