题目
The weights, x kg, of each of 10 watermelons selected at random from Priya’s shop were recorded. The results are summarised as follows
(a) Calculate unbiased estimates of the mean and the variance of the weights of the watermelons in Priya’s shop.
Priya researches the weight of watermelons, for the variety she has in her shop, and discovers that the weights of these watermelons are normally distributed with a standard deviation of 0.8 kg
(b) Calculate a 95% confidence interval for the mean weight of watermelons in Priya’s shop. Give the limits of your confidence interval to 2 decimal places.
Priya claims that the confidence interval in part (b) suggests that nearly all of the watermelons in her shop weigh more than 10.5 kg
(c) Use your answer to part (b) to estimate the smallest proportion of watermelons in her shop that weigh less than 10.5 kg
题目中文翻译
Priya 商店里随机抽取了 10 个西瓜并称重，重量为 x 千克。结果汇总如下：
(a) 求 Priya 商店中这些西瓜重量的均值和方差的无偏估计。
Priya 调查了她店里这种品种西瓜的重量，并发现这些西瓜重量服从标准差为 0.8 千克的正态分布。
(b) 求 Priya 商店中西瓜平均重量的 95% 置信区间。将置信区间的上下限保留 2 位小数。
Priya 认为 (b) 小题中的置信区间表明，她店里几乎所有西瓜都重于 10.5 千克。
(c) 利用 (b) 小题的答案，估计她店里重量小于 10.5 千克的西瓜所占的最小比例。