题目
A shop sells shoes at a mean rate of 4 pairs of shoes per hour on a weekday.
(a) Suggest a suitable distribution for modelling the number of sales of pairs of shoes made per hour on a weekday.
(b) State one assumption necessary for this distribution to be a suitable model of this situation.
(c) Find the probability that on a weekday the shop sells
(i) more than 4 pairs of shoes in a one-hour period,
(ii) more than 4 pairs of shoes in each of 3 consecutive one-hour periods.
The area manager visits the shop on a weekday, the day after an advert for the shop appears in a local paper.
In a one-hour period during the manager’s visit, the shop sells 7 pairs of shoes. This leads the manager to believe that the advert has increased the shop’s sales of pairs of shoes.
(d) Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence of an increase in sales of pairs of shoes following the appearance of the advert.
题目中文翻译
某鞋店在工作日的平均销售速率为每小时 4 双鞋。
(a) 建议一个适合建模工作日每小时售出鞋双数的分布。
(b) 写出该分布作为这个情境的合适模型所必需的一个假设。
(c) 求下列概率：
(i) 在一个小时内售出超过 4 双鞋；
(ii) 在连续 3 个一小时区间内，每个区间都售出超过 4 双鞋。
区域经理在某个工作日到店拜访，恰好是在一则广告刊登在当地报纸后的第二天。
在经理来访期间的一小时内，店里卖出了 7 双鞋。 这使经理相信该广告提高了鞋店的销售量。
(d) 清楚写出假设，在 5% 显著性水平下检验：在广告刊登后，是否有证据表明鞋双销量增加。