题目
A research project into food purchases found that 35% of people who buy eggs do not buy free range eggs.
A random sample of 30 people who bought eggs is taken. The random variable F denotes the number of people who do not buy free range eggs.
(a) Find P(F ≥ 12)
(b) Find P(8 ≤ F < 15)
A farm shop gives 3 loyalty points with every purchase of free range eggs. With every purchase of eggs that are not free range the farm shop gives 1 loyalty point.
A random sample of 30 customers who buy eggs from the farm shop is taken.
(c) Find the probability that the total number of points given to these customers is less than 70
The manager of the farm shop believes that the proportion of customers who buy eggs but do not buy free range eggs is more than 35%
In a survey of 200 customers who buy eggs, 86 do not buy free range eggs.
Using a suitable test and a normal approximation,
(d) determine, at the 5% level of significance, whether there is evidence to support the manager’s belief. State your hypotheses clearly.
(Total for Question 1 is 14 marks)
题目中文翻译
一项关于食物购买的研究发现，在购买鸡蛋的人中，有 35% 的人不购买散养鸡蛋。
随机抽取 30 名购买了鸡蛋的人。随机变量 F 表示其中不购买散养鸡蛋的人数。
(a) 求 。
(b) 求 。
一家农场商店每购买一盒散养鸡蛋给 3 个积分；每购买一盒非散养鸡蛋给 1 个积分。
随机抽取 30 位在该农场商店购买鸡蛋的顾客。
(c) 求这 30 位顾客总共获得的积分少于 70 的概率。
该农场商店经理认为，购买鸡蛋但不购买散养鸡蛋的顾客比例超过 35%。
在对 200 位购买鸡蛋的顾客做调查时，86 人不购买散养鸡蛋。
使用合适的检验和正态近似，
(d) 在 5% 显著性水平下，判断是否有证据支持经理的看法，并清楚写出假设。
（第 1 题共 14 分）